X(x+30)=1600

Solution for X(x+30)=1600 equation:

X(X+30)=1600

We move all terms to the left:

X(X+30)-(1600)=0

We multiply parentheses

X^2+30X-1600=0

a = 1; b = 30; c = -1600;
Δ = b2-4ac
Δ = 302-4·1·(-1600)
Δ = 7300
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:

$\sqrt{\Delta}=\sqrt{7300}=\sqrt{100*73}=\sqrt{100}*\sqrt{73}=10\sqrt{73}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-10\sqrt{73}}{2*1}=\frac{-30-10\sqrt{73}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+10\sqrt{73}}{2*1}=\frac{-30+10\sqrt{73}}{2}
$