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-16x^2+118x+3=0
a = -16; b = 118; c = +3;
Δ = b2-4ac
Δ = 1182-4·(-16)·3
Δ = 14116
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{14116}=\sqrt{4*3529}=\sqrt{4}*\sqrt{3529}=2\sqrt{3529}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(118)-2\sqrt{3529}}{2*-16}=\frac{-118-2\sqrt{3529}}{-32} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(118)+2\sqrt{3529}}{2*-16}=\frac{-118+2\sqrt{3529}}{-32} $
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