4x(x+2)=14-2(3-2x)

Solution for 4x(x+2)=14-2(3-2x) equation:

4x(x+2)=14-2(3-2x)

We move all terms to the left:

4x(x+2)-(14-2(3-2x))=0

We add all the numbers together, and all the variables

4x(x+2)-(14-2(-2x+3))=0

We multiply parentheses

4x^2+8x-(14-2(-2x+3))=0


We calculate terms in parentheses: -(14-2(-2x+3)), so:

14-2(-2x+3)

determiningTheFunctionDomain
-2(-2x+3)+14

We multiply parentheses

4x-6+14

We add all the numbers together, and all the variables

4x+8

Back to the equation:

-(4x+8)


We get rid of parentheses

4x^2+8x-4x-8=0

We add all the numbers together, and all the variables

4x^2+4x-8=0

a = 4; b = 4; c = -8;
Δ = b2-4ac
Δ = 42-4·4·(-8)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-12}{2*4}=\frac{-16}{8}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+12}{2*4}=\frac{8}{8}
=1
$