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X^2-12X+30=23
We move all terms to the left:
X^2-12X+30-(23)=0
We add all the numbers together, and all the variables
X^2-12X+7=0
a = 1; b = -12; c = +7;
Δ = b2-4ac
Δ = -122-4·1·7
Δ = 116
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{116}=\sqrt{4*29}=\sqrt{4}*\sqrt{29}=2\sqrt{29}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{29}}{2*1}=\frac{12-2\sqrt{29}}{2} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{29}}{2*1}=\frac{12+2\sqrt{29}}{2} $
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