(x-5)(4x-10)=0

Solution for (x-5)(4x-10)=0 equation:

(x-5)(4x-10)=0

We multiply parentheses ..

(+4x^2-10x-20x+50)=0

We get rid of parentheses

4x^2-10x-20x+50=0

We add all the numbers together, and all the variables

4x^2-30x+50=0

a = 4; b = -30; c = +50;
Δ = b2-4ac
Δ = -302-4·4·50
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-10}{2*4}=\frac{20}{8}
=2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+10}{2*4}=\frac{40}{8}
=5
$