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6x^2+42x-114=0
a = 6; b = 42; c = -114;
Δ = b2-4ac
Δ = 422-4·6·(-114)
Δ = 4500
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4500}=\sqrt{900*5}=\sqrt{900}*\sqrt{5}=30\sqrt{5}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-30\sqrt{5}}{2*6}=\frac{-42-30\sqrt{5}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+30\sqrt{5}}{2*6}=\frac{-42+30\sqrt{5}}{12} $
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