4x^2-6x-15=0

Simple and best practice solution for 4x^2-6x-15=0 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 4x^2-6x-15=0 equation: 


Simplifying
4x2 + -6x + -15 = 0

Reorder the terms:
-15 + -6x + 4x2 = 0

Solving
-15 + -6x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
-3.75 + -1.5x + x2 = 0

Move the constant term to the right:

Add '3.75' to each side of the equation.
-3.75 + -1.5x + 3.75 + x2 = 0 + 3.75

Reorder the terms:
-3.75 + 3.75 + -1.5x + x2 = 0 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + -1.5x + x2 = 0 + 3.75
-1.5x + x2 = 0 + 3.75

Combine like terms: 0 + 3.75 = 3.75
-1.5x + x2 = 3.75

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 = 3.75 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = 3.75 + 0.5625

Combine like terms: 3.75 + 0.5625 = 4.3125
0.5625 + -1.5x + x2 = 4.3125

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = 4.3125

Calculate the square root of the right side: 2.076655966

Break this problem into two subproblems by setting 
(x + -0.75) equal to 2.076655966 and -2.076655966.


Subproblem 1
x + -0.75 = 2.076655966

Simplifying
x + -0.75 = 2.076655966

Reorder the terms:
-0.75 + x = 2.076655966

Solving
-0.75 + x = 2.076655966

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 = 2.076655966 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = 2.076655966 + 0.75
x = 2.076655966 + 0.75

Combine like terms: 2.076655966 + 0.75 = 2.826655966
x = 2.826655966

Simplifying
x = 2.826655966


Subproblem 2
x + -0.75 = -2.076655966

Simplifying
x + -0.75 = -2.076655966

Reorder the terms:
-0.75 + x = -2.076655966

Solving
-0.75 + x = -2.076655966

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 = -2.076655966 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = -2.076655966 + 0.75
x = -2.076655966 + 0.75

Combine like terms: -2.076655966 + 0.75 = -1.326655966
x = -1.326655966

Simplifying
x = -1.326655966


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.826655966, -1.326655966}

See similar equations:

| 6y-4= | | -2y+28= | | -3x-(5y-3)=-21 | | 5x^2=33x+56 | | y=-1.25(0)+5 | | y=-1.25x+5 | | x+x+2+x=24 | | (x+6)(x-5)=42 | | 0=1.25x+20 | | 0.50x+0.70(50)=0.25(120) | | y=1.25(0)+20 | | g(x)=x+6 | | y+7=2y+5 | | -10.5x/8x= | | x^3+4x-16=0 | | 3(-1/2)= | | X-0.1x+0.06(x-0.1x)=70.79 | | 4x^2+10=1 | | -3(4x-3)+4(6x+1)=43 | | 8-72n^2=0 | | 25+6t=20 | | 3x+30+4x+18=180 | | (4v^3)-(7v^2)-8v+14=0 | | 2x-9=2(x+7) | | 20x-8=36x+4 | | 2+4lnx=7 | | 148500=45x | | 72000=1600x | | -24x^2+40x-14=0 | | X+5=3x+5 | | 3-4=1 | | 1710=1900x |

Equations solver categories