3x+7=-1/3x-4

Solution for 3x+7=-1/3x-4 equation:

3x+7=-1/3x-4

We move all terms to the left:

3x+7-(-1/3x-4)=0


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

x∈R


We get rid of parentheses

3x+1/3x+4+7=0

We multiply all the terms by the denominator


3x*3x+4*3x+7*3x+1=0

Wy multiply elements

9x^2+12x+21x+1=0

We add all the numbers together, and all the variables

9x^2+33x+1=0

a = 9; b = 33; c = +1;
Δ = b2-4ac
Δ = 332-4·9·1
Δ = 1053
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1053}=\sqrt{81*13}=\sqrt{81}*\sqrt{13}=9\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-9\sqrt{13}}{2*9}=\frac{-33-9\sqrt{13}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+9\sqrt{13}}{2*9}=\frac{-33+9\sqrt{13}}{18}
$