a^2+15a=1000

Solution for a^2+15a=1000 equation:

a^2+15a=1000

We move all terms to the left:

a^2+15a-(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:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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