2/3x+14=12x+7

Solution for 2/3x+14=12x+7 equation:

2/3x+14=12x+7

We move all terms to the left:

2/3x+14-(12x+7)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

2/3x-12x-7+14=0

We multiply all the terms by the denominator


-12x*3x-7*3x+14*3x+2=0

Wy multiply elements

-36x^2-21x+42x+2=0

We add all the numbers together, and all the variables

-36x^2+21x+2=0

a = -36; b = 21; c = +2;
Δ = b2-4ac
Δ = 212-4·(-36)·2
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-27}{2*-36}=\frac{-48}{-72}
=2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+27}{2*-36}=\frac{6}{-72}
=-1/12
$