2x+7=-1/3x-7

Solution for 2x+7=-1/3x-7 equation:

2x+7=-1/3x-7

We move all terms to the left:

2x+7-(-1/3x-7)=0


Domain of the equation: 3x-7)!=0

x∈R


We get rid of parentheses

2x+1/3x+7+7=0

We multiply all the terms by the denominator


2x*3x+7*3x+7*3x+1=0

Wy multiply elements

6x^2+21x+21x+1=0

We add all the numbers together, and all the variables

6x^2+42x+1=0

a = 6; b = 42; c = +1;
Δ = b2-4ac
Δ = 422-4·6·1
Δ = 1740
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:

$\sqrt{\Delta}=\sqrt{1740}=\sqrt{4*435}=\sqrt{4}*\sqrt{435}=2\sqrt{435}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-2\sqrt{435}}{2*6}=\frac{-42-2\sqrt{435}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+2\sqrt{435}}{2*6}=\frac{-42+2\sqrt{435}}{12}
$