7/2x-8+1=-4/x-4

Solution for 7/2x-8+1=-4/x-4 equation:

7/2x-8+1=-4/x-4

We move all terms to the left:

7/2x-8+1-(-4/x-4)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



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

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


7x/2x^2+8x/2x^2+4-7=0

We add all the numbers together, and all the variables

7x/2x^2+8x/2x^2-3=0

We multiply all the terms by the denominator


7x+8x-3*2x^2=0

We add all the numbers together, and all the variables

15x-3*2x^2=0

Wy multiply elements

-6x^2+15x=0

a = -6; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·(-6)·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15}{2*-6}=\frac{-30}{-12}
=2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*-6}=\frac{0}{-12}
=0
$