2(x-4)/6x=9x-10

Solution for 2(x-4)/6x=9x-10 equation:

2(x-4)/6x=9x-10

We move all terms to the left:

2(x-4)/6x-(9x-10)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We get rid of parentheses

2(x-4)/6x-9x+10=0

We multiply all the terms by the denominator


2(x-4)-9x*6x+10*6x=0

We multiply parentheses

2x-9x*6x+10*6x-8=0

Wy multiply elements

-54x^2+2x+60x-8=0

We add all the numbers together, and all the variables

-54x^2+62x-8=0

a = -54; b = 62; c = -8;
Δ = b2-4ac
Δ = 622-4·(-54)·(-8)
Δ = 2116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2116}=46$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(62)-46}{2*-54}=\frac{-108}{-108}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(62)+46}{2*-54}=\frac{-16}{-108}
=4/27
$