4x+6=2/2x+3

Solution for 4x+6=2/2x+3 equation:

4x+6=2/2x+3

We move all terms to the left:

4x+6-(2/2x+3)=0


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

x∈R


We get rid of parentheses

4x-2/2x-3+6=0

We multiply all the terms by the denominator


4x*2x-3*2x+6*2x-2=0

Wy multiply elements

8x^2-6x+12x-2=0

We add all the numbers together, and all the variables

8x^2+6x-2=0

a = 8; b = 6; c = -2;
Δ = b2-4ac
Δ = 62-4·8·(-2)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-10}{2*8}=\frac{-16}{16}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+10}{2*8}=\frac{4}{16}
=1/4
$