2x^2-206=-20x

Solution for 2x^2-206=-20x equation:

2x^2-206=-20x

We move all terms to the left:

2x^2-206-(-20x)=0

We get rid of parentheses

2x^2+20x-206=0

a = 2; b = 20; c = -206;
Δ = b2-4ac
Δ = 202-4·2·(-206)
Δ = 2048
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:

$\sqrt{\Delta}=\sqrt{2048}=\sqrt{1024*2}=\sqrt{1024}*\sqrt{2}=32\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-32\sqrt{2}}{2*2}=\frac{-20-32\sqrt{2}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+32\sqrt{2}}{2*2}=\frac{-20+32\sqrt{2}}{4}
$