200x-x^2=15x+7800

Solution for 200x-x^2=15x+7800 equation:

200x-x^2=15x+7800

We move all terms to the left:

200x-x^2-(15x+7800)=0

We add all the numbers together, and all the variables

-1x^2+200x-(15x+7800)=0

We get rid of parentheses

-1x^2+200x-15x-7800=0

We add all the numbers together, and all the variables

-1x^2+185x-7800=0

a = -1; b = 185; c = -7800;
Δ = b2-4ac
Δ = 1852-4·(-1)·(-7800)
Δ = 3025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3025}=55$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(185)-55}{2*-1}=\frac{-240}{-2}
=+120
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(185)+55}{2*-1}=\frac{-130}{-2}
=+65
$