7/x-2+6/2x-4=8

Solution for 7/x-2+6/2x-4=8 equation:

7/x-2+6/2x-4=8

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

7/x+6/2x-14=0

We calculate fractions


14x/2x^2+6x/2x^2-14=0

We multiply all the terms by the denominator


14x+6x-14*2x^2=0

We add all the numbers together, and all the variables

20x-14*2x^2=0

Wy multiply elements

-28x^2+20x=0

a = -28; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·(-28)·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*-28}=\frac{-40}{-56}
=5/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*-28}=\frac{0}{-56}
=0
$