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16x^2+11x-14=0
a = 16; b = 11; c = -14;
Δ = b2-4ac
Δ = 112-4·16·(-14)
Δ = 1017
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1017}=\sqrt{9*113}=\sqrt{9}*\sqrt{113}=3\sqrt{113}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-3\sqrt{113}}{2*16}=\frac{-11-3\sqrt{113}}{32} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+3\sqrt{113}}{2*16}=\frac{-11+3\sqrt{113}}{32} $
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