1/3x+6=2.3x+12

Solution for 1/3x+6=2.3x+12 equation:

1/3x+6=2.3x+12

We move all terms to the left:

1/3x+6-(2.3x+12)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

1/3x-2.3x-12+6=0

We multiply all the terms by the denominator


-(2.3x)*3x-12*3x+6*3x+1=0

We add all the numbers together, and all the variables

-(+2.3x)*3x-12*3x+6*3x+1=0

We multiply parentheses

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

Wy multiply elements

-6x^2-36x+18x+1=0

We add all the numbers together, and all the variables

-6x^2-18x+1=0

a = -6; b = -18; c = +1;
Δ = b2-4ac
Δ = -182-4·(-6)·1
Δ = 348
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:

$\sqrt{\Delta}=\sqrt{348}=\sqrt{4*87}=\sqrt{4}*\sqrt{87}=2\sqrt{87}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{87}}{2*-6}=\frac{18-2\sqrt{87}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{87}}{2*-6}=\frac{18+2\sqrt{87}}{-12}
$