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3x(x+6)=108
We move all terms to the left:
3x(x+6)-(108)=0
We multiply parentheses
3x^2+18x-108=0
a = 3; b = 18; c = -108;
Δ = b2-4ac
Δ = 182-4·3·(-108)
Δ = 1620
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1620}=\sqrt{324*5}=\sqrt{324}*\sqrt{5}=18\sqrt{5}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18\sqrt{5}}{2*3}=\frac{-18-18\sqrt{5}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18\sqrt{5}}{2*3}=\frac{-18+18\sqrt{5}}{6} $
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