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16x^2-24x-107=0
a = 16; b = -24; c = -107;
Δ = b2-4ac
Δ = -242-4·16·(-107)
Δ = 7424
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{7424}=\sqrt{256*29}=\sqrt{256}*\sqrt{29}=16\sqrt{29}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-16\sqrt{29}}{2*16}=\frac{24-16\sqrt{29}}{32} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+16\sqrt{29}}{2*16}=\frac{24+16\sqrt{29}}{32} $
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