3x+5=2/2x+3

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

3x+5=2/2x+3

We move all terms to the left:

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


Domain of the equation: 2x+3)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

6x^2-6x+10x-2=0

We add all the numbers together, and all the variables

6x^2+4x-2=0

a = 6; b = 4; c = -2;
Δ = b2-4ac
Δ = 42-4·6·(-2)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-8}{2*6}=\frac{-12}{12}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+8}{2*6}=\frac{4}{12}
=1/3
$