2/3x+2=126x-3

Solution for 2/3x+2=126x-3 equation:

2/3x+2=126x-3

We move all terms to the left:

2/3x+2-(126x-3)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

2/3x-126x+3+2=0

We multiply all the terms by the denominator


-126x*3x+3*3x+2*3x+2=0

Wy multiply elements

-378x^2+9x+6x+2=0

We add all the numbers together, and all the variables

-378x^2+15x+2=0

a = -378; b = 15; c = +2;
Δ = b2-4ac
Δ = 152-4·(-378)·2
Δ = 3249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3249}=57$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-57}{2*-378}=\frac{-72}{-756}
=2/21
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+57}{2*-378}=\frac{42}{-756}
=-1/18
$