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15x^2+114x+114=0
a = 15; b = 114; c = +114;
Δ = b2-4ac
Δ = 1142-4·15·114
Δ = 6156
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{6156}=\sqrt{324*19}=\sqrt{324}*\sqrt{19}=18\sqrt{19}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(114)-18\sqrt{19}}{2*15}=\frac{-114-18\sqrt{19}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(114)+18\sqrt{19}}{2*15}=\frac{-114+18\sqrt{19}}{30} $
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