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-3x^2+18x=-30
We move all terms to the left:
-3x^2+18x-(-30)=0
We add all the numbers together, and all the variables
-3x^2+18x+30=0
a = -3; b = 18; c = +30;
Δ = b2-4ac
Δ = 182-4·(-3)·30
Δ = 684
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{684}=\sqrt{36*19}=\sqrt{36}*\sqrt{19}=6\sqrt{19}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-6\sqrt{19}}{2*-3}=\frac{-18-6\sqrt{19}}{-6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6\sqrt{19}}{2*-3}=\frac{-18+6\sqrt{19}}{-6} $
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