(5-10x)(9+3x)=0

Solution for (5-10x)(9+3x)=0 equation:

(5-10x)(9+3x)=0

We add all the numbers together, and all the variables

(-10x+5)(3x+9)=0

We multiply parentheses ..

(-30x^2-90x+15x+45)=0

We get rid of parentheses

-30x^2-90x+15x+45=0

We add all the numbers together, and all the variables

-30x^2-75x+45=0

a = -30; b = -75; c = +45;
Δ = b2-4ac
Δ = -752-4·(-30)·45
Δ = 11025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11025}=105$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-75)-105}{2*-30}=\frac{-30}{-60}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+105}{2*-30}=\frac{180}{-60}
=-3
$