93x-16x^2=-46.5

Solution for 93x-16x^2=-46.5 equation:

93x-16x^2=-46.5

We move all terms to the left:

93x-16x^2-(-46.5)=0

We add all the numbers together, and all the variables

-16x^2+93x+46.5=0

a = -16; b = 93; c = +46.5;
Δ = b2-4ac
Δ = 932-4·(-16)·46.5
Δ = 11625
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:

$\sqrt{\Delta}=\sqrt{11625}=\sqrt{25*465}=\sqrt{25}*\sqrt{465}=5\sqrt{465}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(93)-5\sqrt{465}}{2*-16}=\frac{-93-5\sqrt{465}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(93)+5\sqrt{465}}{2*-16}=\frac{-93+5\sqrt{465}}{-32}
$