-16x^2+108x+5=53

Solution for -16x^2+108x+5=53 equation:

-16x^2+108x+5=53

We move all terms to the left:

-16x^2+108x+5-(53)=0

We add all the numbers together, and all the variables

-16x^2+108x-48=0

a = -16; b = 108; c = -48;
Δ = b2-4ac
Δ = 1082-4·(-16)·(-48)
Δ = 8592
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:

$\sqrt{\Delta}=\sqrt{8592}=\sqrt{16*537}=\sqrt{16}*\sqrt{537}=4\sqrt{537}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(108)-4\sqrt{537}}{2*-16}=\frac{-108-4\sqrt{537}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(108)+4\sqrt{537}}{2*-16}=\frac{-108+4\sqrt{537}}{-32}
$