2x+12=5/3x+12=6

Solution for 2x+12=5/3x+12=6 equation:

2x+12=5/3x+12=6

We move all terms to the left:

2x+12-(5/3x+12)=0


Domain of the equation: 3x+12)!=0

x∈R


We get rid of parentheses

2x-5/3x-12+12=0

We multiply all the terms by the denominator


2x*3x-12*3x+12*3x-5=0

Wy multiply elements

6x^2-36x+36x-5=0

We add all the numbers together, and all the variables

6x^2-5=0

a = 6; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·6·(-5)
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{30}}{2*6}=\frac{0-2\sqrt{30}}{12}
=-\frac{2\sqrt{30}}{12}
=-\frac{\sqrt{30}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{30}}{2*6}=\frac{0+2\sqrt{30}}{12}
=\frac{2\sqrt{30}}{12}
=\frac{\sqrt{30}}{6}
$