X(x+40)=600

Solution for X(x+40)=600 equation:

X(X+40)=600

We move all terms to the left:

X(X+40)-(600)=0

We multiply parentheses

X^2+40X-600=0

a = 1; b = 40; c = -600;
Δ = b2-4ac
Δ = 402-4·1·(-600)
Δ = 4000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4000}=\sqrt{400*10}=\sqrt{400}*\sqrt{10}=20\sqrt{10}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-20\sqrt{10}}{2*1}=\frac{-40-20\sqrt{10}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+20\sqrt{10}}{2*1}=\frac{-40+20\sqrt{10}}{2}
$