0=x(2x-3)

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

0=x(2x-3)

We move all terms to the left:

0-(x(2x-3))=0

We add all the numbers together, and all the variables

-(x(2x-3))=0


We calculate terms in parentheses: -(x(2x-3)), so:

x(2x-3)

We multiply parentheses

2x^2-3x

Back to the equation:

-(2x^2-3x)


We get rid of parentheses

-2x^2+3x=0

a = -2; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-2)·0
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{-(3)-3}{2*-2}=\frac{-6}{-4}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-2}=\frac{0}{-4}
=0
$