a(a+3)=100000

Solution for a(a+3)=100000 equation:

a(a+3)=100000

We move all terms to the left:

a(a+3)-(100000)=0

We multiply parentheses

a^2+3a-100000=0

a = 1; b = 3; c = -100000;
Δ = b2-4ac
Δ = 32-4·1·(-100000)
Δ = 400009
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{400009}}{2*1}=\frac{-3-\sqrt{400009}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{400009}}{2*1}=\frac{-3+\sqrt{400009}}{2}
$