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15x^2-15x-120=0
a = 15; b = -15; c = -120;
Δ = b2-4ac
Δ = -152-4·15·(-120)
Δ = 7425
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{7425}=\sqrt{225*33}=\sqrt{225}*\sqrt{33}=15\sqrt{33}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15\sqrt{33}}{2*15}=\frac{15-15\sqrt{33}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15\sqrt{33}}{2*15}=\frac{15+15\sqrt{33}}{30} $
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