7x+1/6x=4x+2/6x-4

Solution for 7x+1/6x=4x+2/6x-4 equation:

7x+1/6x=4x+2/6x-4

We move all terms to the left:

7x+1/6x-(4x+2/6x-4)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 6x-4)!=0

x∈R


We get rid of parentheses

7x+1/6x-4x-2/6x+4=0

We multiply all the terms by the denominator


7x*6x-4x*6x+4*6x+1-2=0

We add all the numbers together, and all the variables

7x*6x-4x*6x+4*6x-1=0

Wy multiply elements

42x^2-24x^2+24x-1=0

We add all the numbers together, and all the variables

18x^2+24x-1=0

a = 18; b = 24; c = -1;
Δ = b2-4ac
Δ = 242-4·18·(-1)
Δ = 648
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:

$\sqrt{\Delta}=\sqrt{648}=\sqrt{324*2}=\sqrt{324}*\sqrt{2}=18\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-18\sqrt{2}}{2*18}=\frac{-24-18\sqrt{2}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+18\sqrt{2}}{2*18}=\frac{-24+18\sqrt{2}}{36}
$