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(X-1)(X+1)+16=12X
We move all terms to the left:
(X-1)(X+1)+16-(12X)=0
We add all the numbers together, and all the variables
-12X+(X-1)(X+1)+16=0
We use the square of the difference formula
X^2-12X-1+16=0
We add all the numbers together, and all the variables
X^2-12X+15=0
a = 1; b = -12; c = +15;
Δ = b2-4ac
Δ = -122-4·1·15
Δ = 84
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{21}}{2*1}=\frac{12-2\sqrt{21}}{2} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{21}}{2*1}=\frac{12+2\sqrt{21}}{2} $
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