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6x^2=-6x+120
We move all terms to the left:
6x^2-(-6x+120)=0
We get rid of parentheses
6x^2+6x-120=0
a = 6; b = 6; c = -120;
Δ = b2-4ac
Δ = 62-4·6·(-120)
Δ = 2916
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{2916}=54$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-54}{2*6}=\frac{-60}{12} =-5 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+54}{2*6}=\frac{48}{12} =4 $
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