(x^2-4)-(x-2)(3-2x)=0

Solution for (x^2-4)-(x-2)(3-2x)=0 equation:

(x^2-4)-(x-2)(3-2x)=0

We add all the numbers together, and all the variables

(x^2-4)-(x-2)(-2x+3)=0

We get rid of parentheses

x^2-(x-2)(-2x+3)-4=0

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

3x^2-7x+2=0

a = 3; b = -7; c = +2;
Δ = b2-4ac
Δ = -72-4·3·2
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{-(-7)-5}{2*3}=\frac{2}{6}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+5}{2*3}=\frac{12}{6}
=2
$