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

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

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

We move all terms to the left:

2/3(x)+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}
$