2x+1=2/3x+5

Solution for 2x+1=2/3x+5 equation:

2x+1=2/3x+5

We move all terms to the left:

2x+1-(2/3x+5)=0


Domain of the equation: 3x+5)!=0

x∈R


We get rid of parentheses

2x-2/3x-5+1=0

We multiply all the terms by the denominator


2x*3x-5*3x+1*3x-2=0

Wy multiply elements

6x^2-15x+3x-2=0

We add all the numbers together, and all the variables

6x^2-12x-2=0

a = 6; b = -12; c = -2;
Δ = b2-4ac
Δ = -122-4·6·(-2)
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-8\sqrt{3}}{2*6}=\frac{12-8\sqrt{3}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+8\sqrt{3}}{2*6}=\frac{12+8\sqrt{3}}{12}
$