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 add all the numbers together, and all the variables

X^2-22X+75=0

a = 1; b = -22; c = +75;
Δ = b2-4ac
Δ = -222-4·1·75
Δ = 184
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:

$\sqrt{\Delta}=\sqrt{184}=\sqrt{4*46}=\sqrt{4}*\sqrt{46}=2\sqrt{46}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{46}}{2*1}=\frac{22-2\sqrt{46}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{46}}{2*1}=\frac{22+2\sqrt{46}}{2}
$