10x(x-2)=90

Solution for 10x(x-2)=90 equation:

10x(x-2)=90

We move all terms to the left:

10x(x-2)-(90)=0

We multiply parentheses

10x^2-20x-90=0

a = 10; b = -20; c = -90;
Δ = b2-4ac
Δ = -202-4·10·(-90)
Δ = 4000
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:

$\sqrt{\Delta}=\sqrt{4000}=\sqrt{400*10}=\sqrt{400}*\sqrt{10}=20\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20\sqrt{10}}{2*10}=\frac{20-20\sqrt{10}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20\sqrt{10}}{2*10}=\frac{20+20\sqrt{10}}{20}
$