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

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

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

We move all terms to the left:

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


Domain of the equation: 3x-4)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

6x^2+12x+9x+2=0

We add all the numbers together, and all the variables

6x^2+21x+2=0

a = 6; b = 21; c = +2;
Δ = b2-4ac
Δ = 212-4·6·2
Δ = 393
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-\sqrt{393}}{2*6}=\frac{-21-\sqrt{393}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{393}}{2*6}=\frac{-21+\sqrt{393}}{12}
$