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

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

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

We move all terms to the left:

3+3/2x-(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

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

a = -8; b = 6; c = +8;
Δ = b2-4ac
Δ = 62-4·(-8)·8
Δ = 292
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:

$\sqrt{\Delta}=\sqrt{292}=\sqrt{4*73}=\sqrt{4}*\sqrt{73}=2\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{73}}{2*-8}=\frac{-6-2\sqrt{73}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{73}}{2*-8}=\frac{-6+2\sqrt{73}}{-16}
$