5x(x-1)-2(2x2-7x)=x-8

Solution for 5x(x-1)-2(2x2-7x)=x-8 equation:

5x(x-1)-2(2x^2-7x)=x-8

We move all terms to the left:

5x(x-1)-2(2x^2-7x)-(x-8)=0

We multiply parentheses

5x^2-4x^2-5x+14x-(x-8)=0

We get rid of parentheses

5x^2-4x^2-5x+14x-x+8=0

We add all the numbers together, and all the variables

x^2+8x+8=0

a = 1; b = 8; c = +8;
Δ = b2-4ac
Δ = 82-4·1·8
Δ = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{2}}{2*1}=\frac{-8-4\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{2}}{2*1}=\frac{-8+4\sqrt{2}}{2}
$