X(x+40)=4500

Solution for X(x+40)=4500 equation:

X(X+40)=4500

We move all terms to the left:

X(X+40)-(4500)=0

We multiply parentheses

X^2+40X-4500=0

a = 1; b = 40; c = -4500;
Δ = b2-4ac
Δ = 402-4·1·(-4500)
Δ = 19600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{19600}=140$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-140}{2*1}=\frac{-180}{2}
=-90
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+140}{2*1}=\frac{100}{2}
=50
$