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4x^2+54x-120=0
a = 4; b = 54; c = -120;
Δ = b2-4ac
Δ = 542-4·4·(-120)
Δ = 4836
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4836}=\sqrt{4*1209}=\sqrt{4}*\sqrt{1209}=2\sqrt{1209}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-2\sqrt{1209}}{2*4}=\frac{-54-2\sqrt{1209}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+2\sqrt{1209}}{2*4}=\frac{-54+2\sqrt{1209}}{8} $
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