x(x+60)=160

Solution for x(x+60)=160 equation:

x(x+60)=160

We move all terms to the left:

x(x+60)-(160)=0

We multiply parentheses

x^2+60x-160=0

a = 1; b = 60; c = -160;
Δ = b2-4ac
Δ = 602-4·1·(-160)
Δ = 4240
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:

$\sqrt{\Delta}=\sqrt{4240}=\sqrt{16*265}=\sqrt{16}*\sqrt{265}=4\sqrt{265}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-4\sqrt{265}}{2*1}=\frac{-60-4\sqrt{265}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+4\sqrt{265}}{2*1}=\frac{-60+4\sqrt{265}}{2}
$