-16x^2+74x+65=150

Solution for -16x^2+74x+65=150 equation:

-16x^2+74x+65=150

We move all terms to the left:

-16x^2+74x+65-(150)=0

We add all the numbers together, and all the variables

-16x^2+74x-85=0

a = -16; b = 74; c = -85;
Δ = b2-4ac
Δ = 742-4·(-16)·(-85)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(74)-6}{2*-16}=\frac{-80}{-32}
=2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(74)+6}{2*-16}=\frac{-68}{-32}
=2+1/8
$