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6x(x+12)=180
We move all terms to the left:
6x(x+12)-(180)=0
We multiply parentheses
6x^2+72x-180=0
a = 6; b = 72; c = -180;
Δ = b2-4ac
Δ = 722-4·6·(-180)
Δ = 9504
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{9504}=\sqrt{144*66}=\sqrt{144}*\sqrt{66}=12\sqrt{66}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-12\sqrt{66}}{2*6}=\frac{-72-12\sqrt{66}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+12\sqrt{66}}{2*6}=\frac{-72+12\sqrt{66}}{12} $
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