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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We multiply parentheses ..

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


We calculate terms in parentheses: -((-4x^2+6x)), so:

(-4x^2+6x)

We get rid of parentheses

-4x^2+6x

Back to the equation:

-(-4x^2+6x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

4x^2-10x=0

a = 4; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·4·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*4}=\frac{0}{8}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*4}=\frac{20}{8}
=2+1/2
$