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600-4x^2-120x=0
a = -4; b = -120; c = +600;
Δ = b2-4ac
Δ = -1202-4·(-4)·600
Δ = 24000
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{24000}=\sqrt{1600*15}=\sqrt{1600}*\sqrt{15}=40\sqrt{15}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-40\sqrt{15}}{2*-4}=\frac{120-40\sqrt{15}}{-8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+40\sqrt{15}}{2*-4}=\frac{120+40\sqrt{15}}{-8} $
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