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X+(12-X)(12-X)=80
We move all terms to the left:
X+(12-X)(12-X)-(80)=0
We add all the numbers together, and all the variables
X+(-1X+12)(-1X+12)-80=0
We multiply parentheses ..
(+X^2-12X-12X+144)+X-80=0
We get rid of parentheses
X^2-12X-12X+X+144-80=0
We add all the numbers together, and all the variables
X^2-23X+64=0
a = 1; b = -23; c = +64;
Δ = b2-4ac
Δ = -232-4·1·64
Δ = 273
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-\sqrt{273}}{2*1}=\frac{23-\sqrt{273}}{2} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{273}}{2*1}=\frac{23+\sqrt{273}}{2} $
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