172,5-x^2=38x

Solution for 172,5-x^2=38x equation:

172.5-x^2=38x

We move all terms to the left:

172.5-x^2-(38x)=0

We add all the numbers together, and all the variables

-1x^2-38x+172.5=0

a = -1; b = -38; c = +172.5;
Δ = b2-4ac
Δ = -382-4·(-1)·172.5
Δ = 2134
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-\sqrt{2134}}{2*-1}=\frac{38-\sqrt{2134}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+\sqrt{2134}}{2*-1}=\frac{38+\sqrt{2134}}{-2}
$