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3x^2+3x=84
We move all terms to the left:
3x^2+3x-(84)=0
a = 3; b = 3; c = -84;
Δ = b2-4ac
Δ = 32-4·3·(-84)
Δ = 1017
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1017}=\sqrt{9*113}=\sqrt{9}*\sqrt{113}=3\sqrt{113}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{113}}{2*3}=\frac{-3-3\sqrt{113}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{113}}{2*3}=\frac{-3+3\sqrt{113}}{6} $
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