167.5=-4x^2+80x-180

Solution for 167.5=-4x^2+80x-180 equation:

167.5=-4x^2+80x-180

We move all terms to the left:

167.5-(-4x^2+80x-180)=0

We get rid of parentheses

4x^2-80x+180+167.5=0

We add all the numbers together, and all the variables

4x^2-80x+347.5=0

a = 4; b = -80; c = +347.5;
Δ = b2-4ac
Δ = -802-4·4·347.5
Δ = 840
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:

$\sqrt{\Delta}=\sqrt{840}=\sqrt{4*210}=\sqrt{4}*\sqrt{210}=2\sqrt{210}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-2\sqrt{210}}{2*4}=\frac{80-2\sqrt{210}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+2\sqrt{210}}{2*4}=\frac{80+2\sqrt{210}}{8}
$