-16x^2+40x+45=66

Solution for -16x^2+40x+45=66 equation:

-16x^2+40x+45=66

We move all terms to the left:

-16x^2+40x+45-(66)=0

We add all the numbers together, and all the variables

-16x^2+40x-21=0

a = -16; b = 40; c = -21;
Δ = b2-4ac
Δ = 402-4·(-16)·(-21)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-16}{2*-16}=\frac{-56}{-32}
=1+3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+16}{2*-16}=\frac{-24}{-32}
=3/4
$