400-x^2=250+5x

Solution for 400-x^2=250+5x equation:

400-x^2=250+5x

We move all terms to the left:

400-x^2-(250+5x)=0

We add all the numbers together, and all the variables

-x^2-(5x+250)+400=0

We add all the numbers together, and all the variables

-1x^2-(5x+250)+400=0

We get rid of parentheses

-1x^2-5x-250+400=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{-20}{-2}
=+10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+25}{2*-1}=\frac{30}{-2}
=-15
$