2x^2-3x=15

Simple and best practice solution for 2x^2-3x=15 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 2x^2-3x=15 equation:


Simplifying
2x2 + -3x = 15

Reorder the terms:
-3x + 2x2 = 15

Solving
-3x + 2x2 = 15

Solving for variable 'x'.

Reorder the terms:
-15 + -3x + 2x2 = 15 + -15

Combine like terms: 15 + -15 = 0
-15 + -3x + 2x2 = 0

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

Divide each side by '2'.
-7.5 + -1.5x + x2 = 0

Move the constant term to the right:

Add '7.5' to each side of the equation.
-7.5 + -1.5x + 7.5 + x2 = 0 + 7.5

Reorder the terms:
-7.5 + 7.5 + -1.5x + x2 = 0 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + -1.5x + x2 = 0 + 7.5
-1.5x + x2 = 0 + 7.5

Combine like terms: 0 + 7.5 = 7.5
-1.5x + x2 = 7.5

The x term is -1.5x.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5x + 0.5625 + x2 = 7.5 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = 7.5 + 0.5625

Combine like terms: 7.5 + 0.5625 = 8.0625
0.5625 + -1.5x + x2 = 8.0625

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = 8.0625

Calculate the square root of the right side: 2.839454173

Break this problem into two subproblems by setting 
(x + -0.75) equal to 2.839454173 and -2.839454173.

Subproblem 1

x + -0.75 = 2.839454173 Simplifying x + -0.75 = 2.839454173 Reorder the terms: -0.75 + x = 2.839454173 Solving -0.75 + x = 2.839454173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 2.839454173 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 2.839454173 + 0.75 x = 2.839454173 + 0.75 Combine like terms: 2.839454173 + 0.75 = 3.589454173 x = 3.589454173 Simplifying x = 3.589454173

Subproblem 2

x + -0.75 = -2.839454173 Simplifying x + -0.75 = -2.839454173 Reorder the terms: -0.75 + x = -2.839454173 Solving -0.75 + x = -2.839454173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -2.839454173 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -2.839454173 + 0.75 x = -2.839454173 + 0.75 Combine like terms: -2.839454173 + 0.75 = -2.089454173 x = -2.089454173 Simplifying x = -2.089454173

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.589454173, -2.089454173}

See similar equations:

| r+9=x | | 12r+60+18=-54 | | (x-4)(x+3)=-6 | | t=5m+5u | | 2r^2+15r+23=0 | | 12r+60= | | u^2-3uv-108v^2=0 | | x^2+23x+22=0 | | g^2+4gh-60h^2=0 | | 5(2z-4)-7z=37 | | x(x-3)=1 | | 5[12-3(2-y)-2y]=2(1-y) | | 6x-7(x+3)=15 | | 8j-3(4j+6)=10 | | -6=-(x+7) | | 5[6-(5x-3)]+3x=0 | | x-4(2x+3)=16 | | 3x^2-900=0 | | 0.5(x-1)=1.0 | | 3-3(x+2)+2=2 | | a^2+2ab-15b^2=0 | | 5-5x=-3 | | 3.51-6.8x+1.11=22.3 | | 0.99y+2.22-0.09y=6.72 | | 25=7x+1-3x | | 6x-13=85 | | 2p-12=-8 | | -2(p-5)7p=-5 | | 4x^2-8x+9=0 | | 2x-8y=32 | | 3(8+42x)=12 | | 8x+2y=24 |

Equations solver categories