-4x(x+2)+x=3x-8-5x

Solution for -4x(x+2)+x=3x-8-5x equation:

-4x(x+2)+x=3x-8-5x

We move all terms to the left:

-4x(x+2)+x-(3x-8-5x)=0

We add all the numbers together, and all the variables

-4x(x+2)+x-(-2x-8)=0

We add all the numbers together, and all the variables

x-4x(x+2)-(-2x-8)=0

We multiply parentheses

-4x^2+x-8x-(-2x-8)=0

We get rid of parentheses

-4x^2+x-8x+2x+8=0

We add all the numbers together, and all the variables

-4x^2-5x+8=0

a = -4; b = -5; c = +8;
Δ = b2-4ac
Δ = -52-4·(-4)·8
Δ = 153
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-3\sqrt{17}}{2*-4}=\frac{5-3\sqrt{17}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+3\sqrt{17}}{2*-4}=\frac{5+3\sqrt{17}}{-8}
$