X2-22x+22=97

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Solution for X2-22x+22=97 equation: 



X2-22X+22=97

We move all terms to the left:

X2-22X+22-(97)=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 = 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
$

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