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-16x^2-10x+7=0
a = -16; b = -10; c = +7;
Δ = b2-4ac
Δ = -102-4·(-16)·7
Δ = 548
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{548}=\sqrt{4*137}=\sqrt{4}*\sqrt{137}=2\sqrt{137}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{137}}{2*-16}=\frac{10-2\sqrt{137}}{-32} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{137}}{2*-16}=\frac{10+2\sqrt{137}}{-32} $
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