x+1=1/3x-7

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

x+1=1/3x-7

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

3x^2+21x+3x-1=0

We add all the numbers together, and all the variables

3x^2+24x-1=0

a = 3; b = 24; c = -1;
Δ = b2-4ac
Δ = 242-4·3·(-1)
Δ = 588
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:

$\sqrt{\Delta}=\sqrt{588}=\sqrt{196*3}=\sqrt{196}*\sqrt{3}=14\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-14\sqrt{3}}{2*3}=\frac{-24-14\sqrt{3}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+14\sqrt{3}}{2*3}=\frac{-24+14\sqrt{3}}{6}
$