x^2=22x+75

Solution for x^2=22x+75 equation:

x^2=22x+75

We move all terms to the left:

x^2-(22x+75)=0

We get rid of parentheses

x^2-22x-75=0

a = 1; b = -22; c = -75;
Δ = b2-4ac
Δ = -222-4·1·(-75)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-28}{2*1}=\frac{-6}{2}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+28}{2*1}=\frac{50}{2}
=25
$