x^2=20x+69

Solution for x^2=20x+69 equation:

x^2=20x+69

We move all terms to the left:

x^2-(20x+69)=0

We get rid of parentheses

x^2-20x-69=0

a = 1; b = -20; c = -69;
Δ = b2-4ac
Δ = -202-4·1·(-69)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-26}{2*1}=\frac{-6}{2}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+26}{2*1}=\frac{46}{2}
=23
$