7/6x-2=x-4

Solution for 7/6x-2=x-4 equation:

7/6x-2=x-4

We move all terms to the left:

7/6x-2-(x-4)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We get rid of parentheses

7/6x-x+4-2=0

We multiply all the terms by the denominator


-x*6x+4*6x-2*6x+7=0

Wy multiply elements

-6x^2+24x-12x+7=0

We add all the numbers together, and all the variables

-6x^2+12x+7=0

a = -6; b = 12; c = +7;
Δ = b2-4ac
Δ = 122-4·(-6)·7
Δ = 312
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:

$\sqrt{\Delta}=\sqrt{312}=\sqrt{4*78}=\sqrt{4}*\sqrt{78}=2\sqrt{78}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{78}}{2*-6}=\frac{-12-2\sqrt{78}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{78}}{2*-6}=\frac{-12+2\sqrt{78}}{-12}
$