5/3x-6=8+5/12x

Solution for 5/3x-6=8+5/12x equation:

5/3x-6=8+5/12x

We move all terms to the left:

5/3x-6-(8+5/12x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 12x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5/3x-(5/12x+8)-6=0

We get rid of parentheses

5/3x-5/12x-8-6=0

We calculate fractions


60x/36x^2+(-15x)/36x^2-8-6=0

We add all the numbers together, and all the variables

60x/36x^2+(-15x)/36x^2-14=0

We multiply all the terms by the denominator


60x+(-15x)-14*36x^2=0

Wy multiply elements

-504x^2+60x+(-15x)=0

We get rid of parentheses

-504x^2+60x-15x=0

We add all the numbers together, and all the variables

-504x^2+45x=0

a = -504; b = 45; c = 0;
Δ = b2-4ac
Δ = 452-4·(-504)·0
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-45}{2*-504}=\frac{-90}{-1008}
=5/56
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+45}{2*-504}=\frac{0}{-1008}
=0
$