x(x-45)=0

Solution for x(x-45)=0 equation:

x(x-45)=0

We multiply parentheses

x^2-45x=0

a = 1; b = -45; c = 0;
Δ = b2-4ac
Δ = -452-4·1·0
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-45}{2*1}=\frac{0}{2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+45}{2*1}=\frac{90}{2}
=45
$