2x+13=1/3x-7

Solution for 2x+13=1/3x-7 equation:

2x+13=1/3x-7

We move all terms to the left:

2x+13-(1/3x-7)=0


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

x∈R


We get rid of parentheses

2x-1/3x+7+13=0

We multiply all the terms by the denominator


2x*3x+7*3x+13*3x-1=0

Wy multiply elements

6x^2+21x+39x-1=0

We add all the numbers together, and all the variables

6x^2+60x-1=0

a = 6; b = 60; c = -1;
Δ = b2-4ac
Δ = 602-4·6·(-1)
Δ = 3624
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:

$\sqrt{\Delta}=\sqrt{3624}=\sqrt{4*906}=\sqrt{4}*\sqrt{906}=2\sqrt{906}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-2\sqrt{906}}{2*6}=\frac{-60-2\sqrt{906}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+2\sqrt{906}}{2*6}=\frac{-60+2\sqrt{906}}{12}
$