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6x(x+2)=66
We move all terms to the left:
6x(x+2)-(66)=0
We multiply parentheses
6x^2+12x-66=0
a = 6; b = 12; c = -66;
Δ = b2-4ac
Δ = 122-4·6·(-66)
Δ = 1728
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1728}=\sqrt{576*3}=\sqrt{576}*\sqrt{3}=24\sqrt{3}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-24\sqrt{3}}{2*6}=\frac{-12-24\sqrt{3}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+24\sqrt{3}}{2*6}=\frac{-12+24\sqrt{3}}{12} $
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