10x(x-2)=20

Solution for 10x(x-2)=20 equation:

10x(x-2)=20

We move all terms to the left:

10x(x-2)-(20)=0

We multiply parentheses

10x^2-20x-20=0

a = 10; b = -20; c = -20;
Δ = b2-4ac
Δ = -202-4·10·(-20)
Δ = 1200
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:

$\sqrt{\Delta}=\sqrt{1200}=\sqrt{400*3}=\sqrt{400}*\sqrt{3}=20\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20\sqrt{3}}{2*10}=\frac{20-20\sqrt{3}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20\sqrt{3}}{2*10}=\frac{20+20\sqrt{3}}{20}
$