6=2x+2/2x+3

Solution for 6=2x+2/2x+3 equation:

6=2x+2/2x+3

We move all terms to the left:

6-(2x+2/2x+3)=0


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

x∈R


We get rid of parentheses

-2x-2/2x-3+6=0

We multiply all the terms by the denominator


-2x*2x-3*2x+6*2x-2=0

Wy multiply elements

-4x^2-6x+12x-2=0

We add all the numbers together, and all the variables

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

a = -4; b = 6; c = -2;
Δ = b2-4ac
Δ = 62-4·(-4)·(-2)
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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