7/3x-12x=3x+1

Solution for 7/3x-12x=3x+1 equation:

7/3x-12x=3x+1

We move all terms to the left:

7/3x-12x-(3x+1)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-12x+7/3x-(3x+1)=0

We get rid of parentheses

-12x+7/3x-3x-1=0

We multiply all the terms by the denominator


-12x*3x-3x*3x-1*3x+7=0

Wy multiply elements

-36x^2-9x^2-3x+7=0

We add all the numbers together, and all the variables

-45x^2-3x+7=0

a = -45; b = -3; c = +7;
Δ = b2-4ac
Δ = -32-4·(-45)·7
Δ = 1269
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:

$\sqrt{\Delta}=\sqrt{1269}=\sqrt{9*141}=\sqrt{9}*\sqrt{141}=3\sqrt{141}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{141}}{2*-45}=\frac{3-3\sqrt{141}}{-90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{141}}{2*-45}=\frac{3+3\sqrt{141}}{-90}
$