5(x-1)(x-2)=0

Solution for 5(x-1)(x-2)=0 equation:

5(x-1)(x-2)=0

We multiply parentheses ..

5(+x^2-2x-1x+2)=0

We multiply parentheses

5x^2-10x-5x+10=0

We add all the numbers together, and all the variables

5x^2-15x+10=0

a = 5; b = -15; c = +10;
Δ = b2-4ac
Δ = -152-4·5·10
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-5}{2*5}=\frac{10}{10}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+5}{2*5}=\frac{20}{10}
=2
$