(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^2-105x+45=0

a = 30; b = -105; c = +45;
Δ = b2-4ac
Δ = -1052-4·30·45
Δ = 5625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5625}=75$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-105)-75}{2*30}=\frac{30}{60}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-105)+75}{2*30}=\frac{180}{60}
=3
$