-2x(5x+8)+6x/4=x-8=

Solution for -2x(5x+8)+6x/4=x-8= equation:

-2x(5x+8)+6x/4=x-8=

We move all terms to the left:

-2x(5x+8)+6x/4-(x-8)=0

We multiply parentheses

-10x^2-16x+6x/4-(x-8)=0

We get rid of parentheses

-10x^2-16x+6x/4-x+8=0

We multiply all the terms by the denominator


-10x^2*4-16x*4+6x-x*4+8*4=0

We add all the numbers together, and all the variables

-10x^2*4+6x-16x*4-x*4+32=0

Wy multiply elements

-40x^2+6x-64x-4x+32=0

We add all the numbers together, and all the variables

-40x^2-62x+32=0

a = -40; b = -62; c = +32;
Δ = b2-4ac
Δ = -622-4·(-40)·32
Δ = 8964
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:

$\sqrt{\Delta}=\sqrt{8964}=\sqrt{36*249}=\sqrt{36}*\sqrt{249}=6\sqrt{249}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-62)-6\sqrt{249}}{2*-40}=\frac{62-6\sqrt{249}}{-80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-62)+6\sqrt{249}}{2*-40}=\frac{62+6\sqrt{249}}{-80}
$