(a-2)(2a-3)=0

Solution for (a-2)(2a-3)=0 equation:

(a-2)(2a-3)=0

We multiply parentheses ..

(+2a^2-3a-4a+6)=0

We get rid of parentheses

2a^2-3a-4a+6=0

We add all the numbers together, and all the variables

2a^2-7a+6=0

a = 2; b = -7; c = +6;
Δ = b2-4ac
Δ = -72-4·2·6
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-1}{2*2}=\frac{6}{4}
=1+1/2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+1}{2*2}=\frac{8}{4}
=2
$