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-16x^2+12x+52=0
a = -16; b = 12; c = +52;
Δ = b2-4ac
Δ = 122-4·(-16)·52
Δ = 3472
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3472}=\sqrt{16*217}=\sqrt{16}*\sqrt{217}=4\sqrt{217}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{217}}{2*-16}=\frac{-12-4\sqrt{217}}{-32} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{217}}{2*-16}=\frac{-12+4\sqrt{217}}{-32} $
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