(x-15)(x)=1000

Solution for (x-15)(x)=1000 equation:

(x-15)(x)=1000

We move all terms to the left:

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

We multiply parentheses

x^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
$