7/x+2-8/4x-8=9

Solution for 7/x+2-8/4x-8=9 equation:

7/x+2-8/4x-8=9

We move all terms to the left:

7/x+2-8/4x-8-(9)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

7/x-8/4x-15=0

We calculate fractions


28x/4x^2+(-8x)/4x^2-15=0

We multiply all the terms by the denominator


28x+(-8x)-15*4x^2=0

Wy multiply elements

-60x^2+28x+(-8x)=0

We get rid of parentheses

-60x^2+28x-8x=0

We add all the numbers together, and all the variables

-60x^2+20x=0

a = -60; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·(-60)·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*-60}=\frac{-40}{-120}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*-60}=\frac{0}{-120}
=0
$