200+5x=50+x^2

Solution for 200+5x=50+x^2 equation:

200+5x=50+x^2

We move all terms to the left:

200+5x-(50+x^2)=0

We get rid of parentheses

-x^2+5x-50+200=0

We add all the numbers together, and all the variables

-1x^2+5x+150=0

a = -1; b = 5; c = +150;
Δ = b2-4ac
Δ = 52-4·(-1)·150
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-25}{2*-1}=\frac{-30}{-2}
=+15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+25}{2*-1}=\frac{20}{-2}
=-10
$