2.3x-5=1/6x+3

Solution for 2.3x-5=1/6x+3 equation:

2.3x-5=1/6x+3

We move all terms to the left:

2.3x-5-(1/6x+3)=0


Domain of the equation: 6x+3)!=0

x∈R


We get rid of parentheses

2.3x-1/6x-3-5=0

We multiply all the terms by the denominator


(2.3x)*6x-3*6x-5*6x-1=0

We add all the numbers together, and all the variables

(+2.3x)*6x-3*6x-5*6x-1=0

We multiply parentheses

12x^2-3*6x-5*6x-1=0

Wy multiply elements

12x^2-18x-30x-1=0

We add all the numbers together, and all the variables

12x^2-48x-1=0

a = 12; b = -48; c = -1;
Δ = b2-4ac
Δ = -482-4·12·(-1)
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*12}=\frac{48-28\sqrt{3}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+28\sqrt{3}}{2*12}=\frac{48+28\sqrt{3}}{24}
$