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3x^2=53x+84
We move all terms to the left:
3x^2-(53x+84)=0
We get rid of parentheses
3x^2-53x-84=0
a = 3; b = -53; c = -84;
Δ = b2-4ac
Δ = -532-4·3·(-84)
Δ = 3817
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-53)-\sqrt{3817}}{2*3}=\frac{53-\sqrt{3817}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-53)+\sqrt{3817}}{2*3}=\frac{53+\sqrt{3817}}{6} $
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