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360=3x(4x+40)
We move all terms to the left:
360-(3x(4x+40))=0
We calculate terms in parentheses: -(3x(4x+40)), so:We get rid of parentheses
3x(4x+40)
We multiply parentheses
12x^2+120x
Back to the equation:
-(12x^2+120x)
-12x^2-120x+360=0
a = -12; b = -120; c = +360;
Δ = b2-4ac
Δ = -1202-4·(-12)·360
Δ = 31680
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{31680}=\sqrt{576*55}=\sqrt{576}*\sqrt{55}=24\sqrt{55}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-24\sqrt{55}}{2*-12}=\frac{120-24\sqrt{55}}{-24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+24\sqrt{55}}{2*-12}=\frac{120+24\sqrt{55}}{-24} $
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