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x^2-12x+7=97
We move all terms to the left:
x^2-12x+7-(97)=0
We add all the numbers together, and all the variables
x^2-12x-90=0
a = 1; b = -12; c = -90;
Δ = b2-4ac
Δ = -122-4·1·(-90)
Δ = 504
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{504}=\sqrt{36*14}=\sqrt{36}*\sqrt{14}=6\sqrt{14}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6\sqrt{14}}{2*1}=\frac{12-6\sqrt{14}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6\sqrt{14}}{2*1}=\frac{12+6\sqrt{14}}{2} $
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