x^2=800-7x

Solution for x^2=800-7x equation:

x^2=800-7x

We move all terms to the left:

x^2-(800-7x)=0

We add all the numbers together, and all the variables

x^2-(-7x+800)=0

We get rid of parentheses

x^2+7x-800=0

a = 1; b = 7; c = -800;
Δ = b2-4ac
Δ = 72-4·1·(-800)
Δ = 3249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3249}=57$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-57}{2*1}=\frac{-64}{2}
=-32
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+57}{2*1}=\frac{50}{2}
=25
$