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15x^2-46x-10=0
a = 15; b = -46; c = -10;
Δ = b2-4ac
Δ = -462-4·15·(-10)
Δ = 2716
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2716}=\sqrt{4*679}=\sqrt{4}*\sqrt{679}=2\sqrt{679}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-2\sqrt{679}}{2*15}=\frac{46-2\sqrt{679}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+2\sqrt{679}}{2*15}=\frac{46+2\sqrt{679}}{30} $
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