x(x-60)=40

Solution for x(x-60)=40 equation:

x(x-60)=40

We move all terms to the left:

x(x-60)-(40)=0

We multiply parentheses

x^2-60x-40=0

a = 1; b = -60; c = -40;
Δ = b2-4ac
Δ = -602-4·1·(-40)
Δ = 3760
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:

$\sqrt{\Delta}=\sqrt{3760}=\sqrt{16*235}=\sqrt{16}*\sqrt{235}=4\sqrt{235}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-4\sqrt{235}}{2*1}=\frac{60-4\sqrt{235}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+4\sqrt{235}}{2*1}=\frac{60+4\sqrt{235}}{2}
$