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16x^2-120x-180=0
a = 16; b = -120; c = -180;
Δ = b2-4ac
Δ = -1202-4·16·(-180)
Δ = 25920
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{25920}=\sqrt{5184*5}=\sqrt{5184}*\sqrt{5}=72\sqrt{5}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-72\sqrt{5}}{2*16}=\frac{120-72\sqrt{5}}{32} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+72\sqrt{5}}{2*16}=\frac{120+72\sqrt{5}}{32} $
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