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6x^2-95x+150=0
a = 6; b = -95; c = +150;
Δ = b2-4ac
Δ = -952-4·6·150
Δ = 5425
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{5425}=\sqrt{25*217}=\sqrt{25}*\sqrt{217}=5\sqrt{217}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-95)-5\sqrt{217}}{2*6}=\frac{95-5\sqrt{217}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-95)+5\sqrt{217}}{2*6}=\frac{95+5\sqrt{217}}{12} $
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