3x+3/2x+4=4x-5/2x

Solution for 3x+3/2x+4=4x-5/2x equation:

3x+3/2x+4=4x-5/2x

We move all terms to the left:

3x+3/2x+4-(4x-5/2x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3x+3/2x-(+4x-5/2x)+4=0

We get rid of parentheses

3x+3/2x-4x+5/2x+4=0

We multiply all the terms by the denominator


3x*2x-4x*2x+4*2x+3+5=0

We add all the numbers together, and all the variables

3x*2x-4x*2x+4*2x+8=0

Wy multiply elements

6x^2-8x^2+8x+8=0

We add all the numbers together, and all the variables

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

a = -2; b = 8; c = +8;
Δ = b2-4ac
Δ = 82-4·(-2)·8
Δ = 128
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{128}=\sqrt{64*2}=\sqrt{64}*\sqrt{2}=8\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8\sqrt{2}}{2*-2}=\frac{-8-8\sqrt{2}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8\sqrt{2}}{2*-2}=\frac{-8+8\sqrt{2}}{-4}
$