200x-x^2=40x+3375

Solution for 200x-x^2=40x+3375 equation:

200x-x^2=40x+3375

We move all terms to the left:

200x-x^2-(40x+3375)=0

We add all the numbers together, and all the variables

-1x^2+200x-(40x+3375)=0

We get rid of parentheses

-1x^2+200x-40x-3375=0

We add all the numbers together, and all the variables

-1x^2+160x-3375=0

a = -1; b = 160; c = -3375;
Δ = b2-4ac
Δ = 1602-4·(-1)·(-3375)
Δ = 12100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12100}=110$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(160)-110}{2*-1}=\frac{-270}{-2}
=+135
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(160)+110}{2*-1}=\frac{-50}{-2}
=+25
$