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6x^2-50x-12=0
a = 6; b = -50; c = -12;
Δ = b2-4ac
Δ = -502-4·6·(-12)
Δ = 2788
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2788}=\sqrt{4*697}=\sqrt{4}*\sqrt{697}=2\sqrt{697}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-2\sqrt{697}}{2*6}=\frac{50-2\sqrt{697}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+2\sqrt{697}}{2*6}=\frac{50+2\sqrt{697}}{12} $
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