8/x-15x=7

Solution for 8/x-15x=7 equation:

8/x-15x=7

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-15x+8/x-7=0

We multiply all the terms by the denominator


-15x*x-7*x+8=0

We add all the numbers together, and all the variables

-7x-15x*x+8=0

Wy multiply elements

-15x^2-7x+8=0

a = -15; b = -7; c = +8;
Δ = b2-4ac
Δ = -72-4·(-15)·8
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{-(-7)-23}{2*-15}=\frac{-16}{-30}
=8/15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+23}{2*-15}=\frac{30}{-30}
=-1
$