3x-11=7/3x+31

Solution for 3x-11=7/3x+31 equation:

3x-11=7/3x+31

We move all terms to the left:

3x-11-(7/3x+31)=0


Domain of the equation: 3x+31)!=0

x∈R


We get rid of parentheses

3x-7/3x-31-11=0

We multiply all the terms by the denominator


3x*3x-31*3x-11*3x-7=0

Wy multiply elements

9x^2-93x-33x-7=0

We add all the numbers together, and all the variables

9x^2-126x-7=0

a = 9; b = -126; c = -7;
Δ = b2-4ac
Δ = -1262-4·9·(-7)
Δ = 16128
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:

$\sqrt{\Delta}=\sqrt{16128}=\sqrt{2304*7}=\sqrt{2304}*\sqrt{7}=48\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-126)-48\sqrt{7}}{2*9}=\frac{126-48\sqrt{7}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-126)+48\sqrt{7}}{2*9}=\frac{126+48\sqrt{7}}{18}
$