x/6x+3=5x-8

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

x/6x+3=5x-8

We move all terms to the left:

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


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


x-5x*6x+8*6x+3*6x=0

Wy multiply elements

-30x^2+x+48x+18x=0

We add all the numbers together, and all the variables

-30x^2+67x=0

a = -30; b = 67; c = 0;
Δ = b2-4ac
Δ = 672-4·(-30)·0
Δ = 4489
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4489}=67$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(67)-67}{2*-30}=\frac{-134}{-60}
=2+7/30
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(67)+67}{2*-30}=\frac{0}{-60}
=0
$