X(60+x)=1600

Solution for X(60+x)=1600 equation:

X(60+X)=1600

We move all terms to the left:

X(60+X)-(1600)=0

We add all the numbers together, and all the variables

X(X+60)-1600=0

We multiply parentheses

X^2+60X-1600=0

a = 1; b = 60; c = -1600;
Δ = b2-4ac
Δ = 602-4·1·(-1600)
Δ = 10000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10000}=100$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-100}{2*1}=\frac{-160}{2}
=-80
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+100}{2*1}=\frac{40}{2}
=20
$