7/x-4/6x=8

Solution for 7/x-4/6x=8 equation:

7/x-4/6x=8

We move all terms to the left:

7/x-4/6x-(8)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We calculate fractions


42x/6x^2+(-4x)/6x^2-8=0

We multiply all the terms by the denominator


42x+(-4x)-8*6x^2=0

Wy multiply elements

-48x^2+42x+(-4x)=0

We get rid of parentheses

-48x^2+42x-4x=0

We add all the numbers together, and all the variables

-48x^2+38x=0

a = -48; b = 38; c = 0;
Δ = b2-4ac
Δ = 382-4·(-48)·0
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-38}{2*-48}=\frac{-76}{-96}
=19/24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+38}{2*-48}=\frac{0}{-96}
=0
$