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

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

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

5x^2-7x+2=0

a = 5; b = -7; c = +2;
Δ = b2-4ac
Δ = -72-4·5·2
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-3}{2*5}=\frac{4}{10}
=2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+3}{2*5}=\frac{10}{10}
=1
$