-16x^2+82x+16=48

Solution for -16x^2+82x+16=48 equation:

-16x^2+82x+16=48

We move all terms to the left:

-16x^2+82x+16-(48)=0

We add all the numbers together, and all the variables

-16x^2+82x-32=0

a = -16; b = 82; c = -32;
Δ = b2-4ac
Δ = 822-4·(-16)·(-32)
Δ = 4676
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:

$\sqrt{\Delta}=\sqrt{4676}=\sqrt{4*1169}=\sqrt{4}*\sqrt{1169}=2\sqrt{1169}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(82)-2\sqrt{1169}}{2*-16}=\frac{-82-2\sqrt{1169}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(82)+2\sqrt{1169}}{2*-16}=\frac{-82+2\sqrt{1169}}{-32}
$