8a^2=4a+3

Simple and best practice solution for 8a^2=4a+3 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for 8a^2=4a+3 equation:


Simplifying
8a2 = 4a + 3

Reorder the terms:
8a2 = 3 + 4a

Solving
8a2 = 3 + 4a

Solving for variable 'a'.

Reorder the terms:
-3 + -4a + 8a2 = 3 + 4a + -3 + -4a

Reorder the terms:
-3 + -4a + 8a2 = 3 + -3 + 4a + -4a

Combine like terms: 3 + -3 = 0
-3 + -4a + 8a2 = 0 + 4a + -4a
-3 + -4a + 8a2 = 4a + -4a

Combine like terms: 4a + -4a = 0
-3 + -4a + 8a2 = 0

Begin completing the square.  Divide all terms by
8 the coefficient of the squared term: 

Divide each side by '8'.
-0.375 + -0.5a + a2 = 0

Move the constant term to the right:

Add '0.375' to each side of the equation.
-0.375 + -0.5a + 0.375 + a2 = 0 + 0.375

Reorder the terms:
-0.375 + 0.375 + -0.5a + a2 = 0 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + -0.5a + a2 = 0 + 0.375
-0.5a + a2 = 0 + 0.375

Combine like terms: 0 + 0.375 = 0.375
-0.5a + a2 = 0.375

The a term is -0.5a.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5a + 0.0625 + a2 = 0.375 + 0.0625

Reorder the terms:
0.0625 + -0.5a + a2 = 0.375 + 0.0625

Combine like terms: 0.375 + 0.0625 = 0.4375
0.0625 + -0.5a + a2 = 0.4375

Factor a perfect square on the left side:
(a + -0.25)(a + -0.25) = 0.4375

Calculate the square root of the right side: 0.661437828

Break this problem into two subproblems by setting 
(a + -0.25) equal to 0.661437828 and -0.661437828.

Subproblem 1

a + -0.25 = 0.661437828 Simplifying a + -0.25 = 0.661437828 Reorder the terms: -0.25 + a = 0.661437828 Solving -0.25 + a = 0.661437828 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + a = 0.661437828 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + a = 0.661437828 + 0.25 a = 0.661437828 + 0.25 Combine like terms: 0.661437828 + 0.25 = 0.911437828 a = 0.911437828 Simplifying a = 0.911437828

Subproblem 2

a + -0.25 = -0.661437828 Simplifying a + -0.25 = -0.661437828 Reorder the terms: -0.25 + a = -0.661437828 Solving -0.25 + a = -0.661437828 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + a = -0.661437828 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + a = -0.661437828 + 0.25 a = -0.661437828 + 0.25 Combine like terms: -0.661437828 + 0.25 = -0.411437828 a = -0.411437828 Simplifying a = -0.411437828

Solution

The solution to the problem is based on the solutions from the subproblems. a = {0.911437828, -0.411437828}

See similar equations:

| 7/12÷(-2/3) | | 2b+3b+4b= | | 18.8+x=12 | | 0.25(16x-80)+16-10x=8+3(x-8)-12x | | -8x+2=10x+15 | | 5x^4+29x+36=0 | | 6x^2+5x-9=35 | | F=(9/5)-460 | | 3n^2-n=-6 | | 0.25(16-80)+16-10x=8+3(x-8)-12x | | 7/12÷(-1/4) | | 6(3m+5)= | | 160/28 | | x-12+x-44+x-44+x+x=540 | | 2(3x-8)=5-7x | | 1729/42 | | 7=b/2 | | 2/4*(-5/9) | | 2/8x4/16 | | 3=u/6-6 | | 3(-7)=c+1 | | 14x-25=30 | | Y=-2*1+21 | | (x-11)+(x-44)+(x-44)+x+x=540 | | 2x-3+4x+11=180 | | 7/4*7/4*3/7=x | | 0.3b-21=3.6 | | 2x-3+x+x=180 | | 10x^2+19x+3=0 | | -8x+2=10x+3 | | (10y-8)-(y-4)= | | (x-12)+(x-44)+x+x=540 |

Equations solver categories