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-3x^2+24x+11=0
a = -3; b = 24; c = +11;
Δ = b2-4ac
Δ = 242-4·(-3)·11
Δ = 708
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{708}=\sqrt{4*177}=\sqrt{4}*\sqrt{177}=2\sqrt{177}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{177}}{2*-3}=\frac{-24-2\sqrt{177}}{-6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{177}}{2*-3}=\frac{-24+2\sqrt{177}}{-6} $
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