4/3x+3=-x-4

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

4/3x+3=-x-4

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

4/3x-(-1x-4)+3=0

We get rid of parentheses

4/3x+1x+4+3=0

We multiply all the terms by the denominator


1x*3x+4*3x+3*3x+4=0

Wy multiply elements

3x^2+12x+9x+4=0

We add all the numbers together, and all the variables

3x^2+21x+4=0

a = 3; b = 21; c = +4;
Δ = b2-4ac
Δ = 212-4·3·4
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*3}=\frac{-21-\sqrt{393}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{393}}{2*3}=\frac{-21+\sqrt{393}}{6}
$