x(x-46)=180

Solution for x(x-46)=180 equation:

x(x-46)=180

We move all terms to the left:

x(x-46)-(180)=0

We multiply parentheses

x^2-46x-180=0

a = 1; b = -46; c = -180;
Δ = b2-4ac
Δ = -462-4·1·(-180)
Δ = 2836
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:

$\sqrt{\Delta}=\sqrt{2836}=\sqrt{4*709}=\sqrt{4}*\sqrt{709}=2\sqrt{709}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-2\sqrt{709}}{2*1}=\frac{46-2\sqrt{709}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+2\sqrt{709}}{2*1}=\frac{46+2\sqrt{709}}{2}
$