1000-x*x=15*x

Solution for 1000-x*x=15*x equation:

1000-x*x=15x

We move all terms to the left:

1000-x*x-(15x)=0

We add all the numbers together, and all the variables

-15x-x*x+1000=0

Wy multiply elements

-1x^2-15x+1000=0

a = -1; b = -15; c = +1000;
Δ = b2-4ac
Δ = -152-4·(-1)·1000
Δ = 4225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4225}=65$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-65}{2*-1}=\frac{-50}{-2}
=+25
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+65}{2*-1}=\frac{80}{-2}
=-40
$