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6x+9=x2
We move all terms to the left:
6x+9-(x2)=0
We add all the numbers together, and all the variables
-1x^2+6x+9=0
a = -1; b = 6; c = +9;
Δ = b2-4ac
Δ = 62-4·(-1)·9
Δ = 72
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{2}}{2*-1}=\frac{-6-6\sqrt{2}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{2}}{2*-1}=\frac{-6+6\sqrt{2}}{-2} $
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