3/12x-1=4/5x+6

Solution for 3/12x-1=4/5x+6 equation:

3/12x-1=4/5x+6

We move all terms to the left:

3/12x-1-(4/5x+6)=0


Domain of the equation: 12x!=0

x!=0/12

x!=0

x∈R



Domain of the equation: 5x+6)!=0

x∈R


We get rid of parentheses

3/12x-4/5x-6-1=0

We calculate fractions


15x/60x^2+(-48x)/60x^2-6-1=0

We add all the numbers together, and all the variables

15x/60x^2+(-48x)/60x^2-7=0

We multiply all the terms by the denominator


15x+(-48x)-7*60x^2=0

Wy multiply elements

-420x^2+15x+(-48x)=0

We get rid of parentheses

-420x^2+15x-48x=0

We add all the numbers together, and all the variables

-420x^2-33x=0

a = -420; b = -33; c = 0;
Δ = b2-4ac
Δ = -332-4·(-420)·0
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-33}{2*-420}=\frac{0}{-840}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+33}{2*-420}=\frac{66}{-840}
=-11/140
$