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-16x^2+22x+5=0
a = -16; b = 22; c = +5;
Δ = b2-4ac
Δ = 222-4·(-16)·5
Δ = 804
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{804}=\sqrt{4*201}=\sqrt{4}*\sqrt{201}=2\sqrt{201}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{201}}{2*-16}=\frac{-22-2\sqrt{201}}{-32} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{201}}{2*-16}=\frac{-22+2\sqrt{201}}{-32} $
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