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6x^2-50x-76=0
a = 6; b = -50; c = -76;
Δ = b2-4ac
Δ = -502-4·6·(-76)
Δ = 4324
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4324}=\sqrt{4*1081}=\sqrt{4}*\sqrt{1081}=2\sqrt{1081}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-2\sqrt{1081}}{2*6}=\frac{50-2\sqrt{1081}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+2\sqrt{1081}}{2*6}=\frac{50+2\sqrt{1081}}{12} $
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