112x-16x^2=5

Solution for 112x-16x^2=5 equation:

112x-16x^2=5

We move all terms to the left:

112x-16x^2-(5)=0

a = -16; b = 112; c = -5;
Δ = b2-4ac
Δ = 1122-4·(-16)·(-5)
Δ = 12224
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:

$\sqrt{\Delta}=\sqrt{12224}=\sqrt{64*191}=\sqrt{64}*\sqrt{191}=8\sqrt{191}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(112)-8\sqrt{191}}{2*-16}=\frac{-112-8\sqrt{191}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(112)+8\sqrt{191}}{2*-16}=\frac{-112+8\sqrt{191}}{-32}
$