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2x+6=-66+6x^2
We move all terms to the left:
2x+6-(-66+6x^2)=0
We get rid of parentheses
-6x^2+2x+66+6=0
We add all the numbers together, and all the variables
-6x^2+2x+72=0
a = -6; b = 2; c = +72;
Δ = b2-4ac
Δ = 22-4·(-6)·72
Δ = 1732
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1732}=\sqrt{4*433}=\sqrt{4}*\sqrt{433}=2\sqrt{433}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{433}}{2*-6}=\frac{-2-2\sqrt{433}}{-12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{433}}{2*-6}=\frac{-2+2\sqrt{433}}{-12} $
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