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

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

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

We move all terms to the left:

2/3x+3+4x-(-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

4x+2/3x+7=0

We multiply all the terms by the denominator


4x*3x+7*3x+2=0

Wy multiply elements

12x^2+21x+2=0

a = 12; b = 21; c = +2;
Δ = b2-4ac
Δ = 212-4·12·2
Δ = 345
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{345}}{2*12}=\frac{-21-\sqrt{345}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{345}}{2*12}=\frac{-21+\sqrt{345}}{24}
$