7x/15x+8=1/x

Solution for 7x/15x+8=1/x equation:

7x/15x+8=1/x

We move all terms to the left:

7x/15x+8-(1/x)=0


Domain of the equation: 15x!=0

x!=0/15

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

7x/15x-(+1/x)+8=0

We get rid of parentheses

7x/15x-1/x+8=0

We calculate fractions


7x^2/15x^2+(-15x)/15x^2+8=0

We multiply all the terms by the denominator


7x^2+(-15x)+8*15x^2=0

Wy multiply elements

7x^2+120x^2+(-15x)=0

We get rid of parentheses

7x^2+120x^2-15x=0

We add all the numbers together, and all the variables

127x^2-15x=0

a = 127; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·127·0
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*127}=\frac{0}{254}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*127}=\frac{30}{254}
=15/127
$