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3x^2+6x+9=69
We move all terms to the left:
3x^2+6x+9-(69)=0
We add all the numbers together, and all the variables
3x^2+6x-60=0
a = 3; b = 6; c = -60;
Δ = b2-4ac
Δ = 62-4·3·(-60)
Δ = 756
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{756}=\sqrt{36*21}=\sqrt{36}*\sqrt{21}=6\sqrt{21}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{21}}{2*3}=\frac{-6-6\sqrt{21}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{21}}{2*3}=\frac{-6+6\sqrt{21}}{6} $
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