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6x(x+10)=120
We move all terms to the left:
6x(x+10)-(120)=0
We multiply parentheses
6x^2+60x-120=0
a = 6; b = 60; c = -120;
Δ = b2-4ac
Δ = 602-4·6·(-120)
Δ = 6480
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{6480}=\sqrt{1296*5}=\sqrt{1296}*\sqrt{5}=36\sqrt{5}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-36\sqrt{5}}{2*6}=\frac{-60-36\sqrt{5}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+36\sqrt{5}}{2*6}=\frac{-60+36\sqrt{5}}{12} $
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