7/2x+12+4=-8/x+6

Solution for 7/2x+12+4=-8/x+6 equation:

7/2x+12+4=-8/x+6

We move all terms to the left:

7/2x+12+4-(-8/x+6)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: x+6)!=0

x∈R


We add all the numbers together, and all the variables

7/2x-(-8/x+6)+16=0

We get rid of parentheses

7/2x+8/x-6+16=0

We calculate fractions


7x/2x^2+16x/2x^2-6+16=0

We add all the numbers together, and all the variables

7x/2x^2+16x/2x^2+10=0

We multiply all the terms by the denominator


7x+16x+10*2x^2=0

We add all the numbers together, and all the variables

23x+10*2x^2=0

Wy multiply elements

20x^2+23x=0

a = 20; b = 23; c = 0;
Δ = b2-4ac
Δ = 232-4·20·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-23}{2*20}=\frac{-46}{40}
=-1+3/20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+23}{2*20}=\frac{0}{40}
=0
$