15+x/x+7=x+7/x

Solution for 15+x/x+7=x+7/x equation:

15+x/x+7=x+7/x

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x/x-(+x+7/x)+15+7=0

We add all the numbers together, and all the variables

x/x-(+x+7/x)+22=0

We get rid of parentheses

x/x-x-7/x+22=0

Fractions to decimals

-7/x-x+22+1=0

We multiply all the terms by the denominator


-x*x+22*x+1*x-7=0

We add all the numbers together, and all the variables

23x-x*x-7=0

Wy multiply elements

-1x^2+23x-7=0

a = -1; b = 23; c = -7;
Δ = b2-4ac
Δ = 232-4·(-1)·(-7)
Δ = 501
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-\sqrt{501}}{2*-1}=\frac{-23-\sqrt{501}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+\sqrt{501}}{2*-1}=\frac{-23+\sqrt{501}}{-2}
$