x^2+97=20x

Solution for x^2+97=20x equation:

x^2+97=20x

We move all terms to the left:

x^2+97-(20x)=0

a = 1; b = -20; c = +97;
Δ = b2-4ac
Δ = -202-4·1·97
Δ = 12
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:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{3}}{2*1}=\frac{20-2\sqrt{3}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{3}}{2*1}=\frac{20+2\sqrt{3}}{2}
$