(3-2x)(2x+4)=(2x-3)(3-9x)

Solution for (3-2x)(2x+4)=(2x-3)(3-9x) equation:

(3-2x)(2x+4)=(2x-3)(3-9x)

We move all terms to the left:

(3-2x)(2x+4)-((2x-3)(3-9x))=0

We add all the numbers together, and all the variables

(-2x+3)(2x+4)-((2x-3)(-9x+3))=0

We multiply parentheses ..

(-4x^2-8x+6x+12)-((2x-3)(-9x+3))=0


We calculate terms in parentheses: -((2x-3)(-9x+3)), so:

(2x-3)(-9x+3)

We multiply parentheses ..

(-18x^2+6x+27x-9)

We get rid of parentheses

-18x^2+6x+27x-9

We add all the numbers together, and all the variables

-18x^2+33x-9

Back to the equation:

-(-18x^2+33x-9)


We get rid of parentheses

-4x^2+18x^2-8x+6x-33x+12+9=0

We add all the numbers together, and all the variables

14x^2-35x+21=0

a = 14; b = -35; c = +21;
Δ = b2-4ac
Δ = -352-4·14·21
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-7}{2*14}=\frac{28}{28}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+7}{2*14}=\frac{42}{28}
=1+1/2
$