5x(x-8)-8x=-10

Solution for 5x(x-8)-8x=-10 equation:

5x(x-8)-8x=-10

We move all terms to the left:

5x(x-8)-8x-(-10)=0

We add all the numbers together, and all the variables

-8x+5x(x-8)+10=0

We multiply parentheses

5x^2-8x-40x+10=0

We add all the numbers together, and all the variables

5x^2-48x+10=0

a = 5; b = -48; c = +10;
Δ = b2-4ac
Δ = -482-4·5·10
Δ = 2104
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:

$\sqrt{\Delta}=\sqrt{2104}=\sqrt{4*526}=\sqrt{4}*\sqrt{526}=2\sqrt{526}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-2\sqrt{526}}{2*5}=\frac{48-2\sqrt{526}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+2\sqrt{526}}{2*5}=\frac{48+2\sqrt{526}}{10}
$