-5x(2x-9)=0

Solution for -5x(2x-9)=0 equation:

-5x(2x-9)=0

We multiply parentheses

-10x^2+45x=0

a = -10; b = 45; c = 0;
Δ = b2-4ac
Δ = 452-4·(-10)·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*-10}=\frac{-90}{-20}
=4+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+45}{2*-10}=\frac{0}{-20}
=0
$