1/3x+11=2x-7

Solution for 1/3x+11=2x-7 equation:

1/3x+11=2x-7

We move all terms to the left:

1/3x+11-(2x-7)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

1/3x-2x+7+11=0

We multiply all the terms by the denominator


-2x*3x+7*3x+11*3x+1=0

Wy multiply elements

-6x^2+21x+33x+1=0

We add all the numbers together, and all the variables

-6x^2+54x+1=0

a = -6; b = 54; c = +1;
Δ = b2-4ac
Δ = 542-4·(-6)·1
Δ = 2940
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:

$\sqrt{\Delta}=\sqrt{2940}=\sqrt{196*15}=\sqrt{196}*\sqrt{15}=14\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-14\sqrt{15}}{2*-6}=\frac{-54-14\sqrt{15}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+14\sqrt{15}}{2*-6}=\frac{-54+14\sqrt{15}}{-12}
$