185x-2x^2=-x^2+7500

Solution for 185x-2x^2=-x^2+7500 equation:

185x-2x^2=-x^2+7500

We move all terms to the left:

185x-2x^2-(-x^2+7500)=0

We get rid of parentheses

-2x^2+x^2+185x-7500=0

We add all the numbers together, and all the variables

-1x^2+185x-7500=0

a = -1; b = 185; c = -7500;
Δ = b2-4ac
Δ = 1852-4·(-1)·(-7500)
Δ = 4225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4225}=65$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(185)-65}{2*-1}=\frac{-250}{-2}
=+125
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(185)+65}{2*-1}=\frac{-120}{-2}
=+60
$