4x(8-x)-2=9x-20+x-5

Solution for 4x(8-x)-2=9x-20+x-5 equation:

4x(8-x)-2=9x-20+x-5

We move all terms to the left:

4x(8-x)-2-(9x-20+x-5)=0

We add all the numbers together, and all the variables

4x(-1x+8)-(10x-25)-2=0

We multiply parentheses

-4x^2+32x-(10x-25)-2=0

We get rid of parentheses

-4x^2+32x-10x+25-2=0

We add all the numbers together, and all the variables

-4x^2+22x+23=0

a = -4; b = 22; c = +23;
Δ = b2-4ac
Δ = 222-4·(-4)·23
Δ = 852
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:

$\sqrt{\Delta}=\sqrt{852}=\sqrt{4*213}=\sqrt{4}*\sqrt{213}=2\sqrt{213}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{213}}{2*-4}=\frac{-22-2\sqrt{213}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{213}}{2*-4}=\frac{-22+2\sqrt{213}}{-8}
$