-4x^2+80x-150=167.5

Solution for -4x^2+80x-150=167.5 equation:

-4x^2+80x-150=167.5

We move all terms to the left:

-4x^2+80x-150-(167.5)=0

We add all the numbers together, and all the variables

-4x^2+80x-317.5=0

a = -4; b = 80; c = -317.5;
Δ = b2-4ac
Δ = 802-4·(-4)·(-317.5)
Δ = 1320
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:

$\sqrt{\Delta}=\sqrt{1320}=\sqrt{4*330}=\sqrt{4}*\sqrt{330}=2\sqrt{330}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-2\sqrt{330}}{2*-4}=\frac{-80-2\sqrt{330}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+2\sqrt{330}}{2*-4}=\frac{-80+2\sqrt{330}}{-8}
$