5x/x(x)x+5=5/x(x)-7

Solution for 5x/x(x)x+5=5/x(x)-7 equation:

5x/x(x)x+5=5/x(x)-7

We move all terms to the left:

5x/x(x)x+5-(5/x(x)-7)=0


Domain of the equation: xxx!=0

x!=0/1

x!=0

x∈R



Domain of the equation: xx-7)!=0

x∈R


We get rid of parentheses

5x/xxx-5/xx+7+5=0

We calculate fractions


5x^2/x^2+(-5x)/x^2+7+5=0

We add all the numbers together, and all the variables

5x^2/x^2+(-5x)/x^2+12=0

We multiply all the terms by the denominator


5x^2+(-5x)+12*x^2=0

We add all the numbers together, and all the variables

17x^2+(-5x)=0

We get rid of parentheses

17x^2-5x=0

a = 17; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·17·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*17}=\frac{0}{34}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*17}=\frac{10}{34}
=5/17
$