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15x^2+10x=120
We move all terms to the left:
15x^2+10x-(120)=0
a = 15; b = 10; c = -120;
Δ = b2-4ac
Δ = 102-4·15·(-120)
Δ = 7300
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{7300}=\sqrt{100*73}=\sqrt{100}*\sqrt{73}=10\sqrt{73}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10\sqrt{73}}{2*15}=\frac{-10-10\sqrt{73}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10\sqrt{73}}{2*15}=\frac{-10+10\sqrt{73}}{30} $
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