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

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

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

We move all terms to the left:

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


We calculate terms in parentheses: -(5x-5x(x-8)), so:

5x-5x(x-8)

We multiply parentheses

-5x^2+5x+40x

We add all the numbers together, and all the variables

-5x^2+45x

Back to the equation:

-(-5x^2+45x)


We get rid of parentheses

5x^2-45x+10=0

a = 5; b = -45; c = +10;
Δ = b2-4ac
Δ = -452-4·5·10
Δ = 1825
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:

$\sqrt{\Delta}=\sqrt{1825}=\sqrt{25*73}=\sqrt{25}*\sqrt{73}=5\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-5\sqrt{73}}{2*5}=\frac{45-5\sqrt{73}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+5\sqrt{73}}{2*5}=\frac{45+5\sqrt{73}}{10}
$