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

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

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

We multiply parentheses ..

(+2x^2-5x-4x+10)=0

We get rid of parentheses

2x^2-5x-4x+10=0

We add all the numbers together, and all the variables

2x^2-9x+10=0

a = 2; b = -9; c = +10;
Δ = b2-4ac
Δ = -92-4·2·10
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-1}{2*2}=\frac{8}{4}
=2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+1}{2*2}=\frac{10}{4}
=2+1/2
$