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3x^2-84x-57=0
a = 3; b = -84; c = -57;
Δ = b2-4ac
Δ = -842-4·3·(-57)
Δ = 7740
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{7740}=\sqrt{36*215}=\sqrt{36}*\sqrt{215}=6\sqrt{215}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-6\sqrt{215}}{2*3}=\frac{84-6\sqrt{215}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+6\sqrt{215}}{2*3}=\frac{84+6\sqrt{215}}{6} $
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