172.5=345-76x+4x^2

Solution for 172.5=345-76x+4x^2 equation:

172.5=345-76x+4x^2

We move all terms to the left:

172.5-(345-76x+4x^2)=0

We get rid of parentheses

-4x^2+76x-345+172.5=0

We add all the numbers together, and all the variables

-4x^2+76x-172.5=0

a = -4; b = 76; c = -172.5;
Δ = b2-4ac
Δ = 762-4·(-4)·(-172.5)
Δ = 3016
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:

$\sqrt{\Delta}=\sqrt{3016}=\sqrt{4*754}=\sqrt{4}*\sqrt{754}=2\sqrt{754}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(76)-2\sqrt{754}}{2*-4}=\frac{-76-2\sqrt{754}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(76)+2\sqrt{754}}{2*-4}=\frac{-76+2\sqrt{754}}{-8}
$