2/3x-5=2x+11

Solution for 2/3x-5=2x+11 equation:

2/3x-5=2x+11

We move all terms to the left:

2/3x-5-(2x+11)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

2/3x-2x-11-5=0

We multiply all the terms by the denominator


-2x*3x-11*3x-5*3x+2=0

Wy multiply elements

-6x^2-33x-15x+2=0

We add all the numbers together, and all the variables

-6x^2-48x+2=0

a = -6; b = -48; c = +2;
Δ = b2-4ac
Δ = -482-4·(-6)·2
Δ = 2352
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:

$\sqrt{\Delta}=\sqrt{2352}=\sqrt{784*3}=\sqrt{784}*\sqrt{3}=28\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-28\sqrt{3}}{2*-6}=\frac{48-28\sqrt{3}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+28\sqrt{3}}{2*-6}=\frac{48+28\sqrt{3}}{-12}
$