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X^2+22X+121=7
We move all terms to the left:
X^2+22X+121-(7)=0
We add all the numbers together, and all the variables
X^2+22X+114=0
a = 1; b = 22; c = +114;
Δ = b2-4ac
Δ = 222-4·1·114
Δ = 28
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{7}}{2*1}=\frac{-22-2\sqrt{7}}{2} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{7}}{2*1}=\frac{-22+2\sqrt{7}}{2} $
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