9x-4/x=15

Solution for 9x-4/x=15 equation:

9x-4/x=15

We move all terms to the left:

9x-4/x-(15)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


9x*x-15*x-4=0

We add all the numbers together, and all the variables

-15x+9x*x-4=0

Wy multiply elements

9x^2-15x-4=0

a = 9; b = -15; c = -4;
Δ = b2-4ac
Δ = -152-4·9·(-4)
Δ = 369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{369}=\sqrt{9*41}=\sqrt{9}*\sqrt{41}=3\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3\sqrt{41}}{2*9}=\frac{15-3\sqrt{41}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3\sqrt{41}}{2*9}=\frac{15+3\sqrt{41}}{18}
$