12x+9=x2

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Solution for 12x+9=x2 equation:



12x+9=x2
We move all terms to the left:
12x+9-(x2)=0
We add all the numbers together, and all the variables
-1x^2+12x+9=0
a = -1; b = 12; c = +9;
Δ = b2-4ac
Δ = 122-4·(-1)·9
Δ = 180
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:
$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-6\sqrt{5}}{2*-1}=\frac{-12-6\sqrt{5}}{-2} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+6\sqrt{5}}{2*-1}=\frac{-12+6\sqrt{5}}{-2} $

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