10x^2-20x=400

Solution for 10x^2-20x=400 equation:

10x^2-20x=400

We move all terms to the left:

10x^2-20x-(400)=0

a = 10; b = -20; c = -400;
Δ = b2-4ac
Δ = -202-4·10·(-400)
Δ = 16400
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:

$\sqrt{\Delta}=\sqrt{16400}=\sqrt{400*41}=\sqrt{400}*\sqrt{41}=20\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20\sqrt{41}}{2*10}=\frac{20-20\sqrt{41}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20\sqrt{41}}{2*10}=\frac{20+20\sqrt{41}}{20}
$