-x^2+15x+6750=200x-2x^2

Solution for -x^2+15x+6750=200x-2x^2 equation:

-x^2+15x+6750=200x-2x^2

We move all terms to the left:

-x^2+15x+6750-(200x-2x^2)=0

We add all the numbers together, and all the variables

-1x^2-(200x-2x^2)+15x+6750=0

We get rid of parentheses

-1x^2+2x^2-200x+15x+6750=0

We add all the numbers together, and all the variables

x^2-185x+6750=0

a = 1; b = -185; c = +6750;
Δ = b2-4ac
Δ = -1852-4·1·6750
Δ = 7225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7225}=85$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-185)-85}{2*1}=\frac{100}{2}
=50
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-185)+85}{2*1}=\frac{270}{2}
=135
$