x2-341=20x

Solution for x2-341=20x equation:

x2-341=20x

We move all terms to the left:

x2-341-(20x)=0

We add all the numbers together, and all the variables

x^2-20x-341=0

a = 1; b = -20; c = -341;
Δ = b2-4ac
Δ = -202-4·1·(-341)
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-42}{2*1}=\frac{-22}{2}
=-11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+42}{2*1}=\frac{62}{2}
=31
$