(10x-30)(5x-25)=0

Solution for (10x-30)(5x-25)=0 equation:

(10x-30)(5x-25)=0

We multiply parentheses ..

(+50x^2-250x-150x+750)=0

We get rid of parentheses

50x^2-250x-150x+750=0

We add all the numbers together, and all the variables

50x^2-400x+750=0

a = 50; b = -400; c = +750;
Δ = b2-4ac
Δ = -4002-4·50·750
Δ = 10000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10000}=100$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-400)-100}{2*50}=\frac{300}{100}
=3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-400)+100}{2*50}=\frac{500}{100}
=5
$