3x-15/x=8

Solution for 3x-15/x=8 equation:

3x-15/x=8

We move all terms to the left:

3x-15/x-(8)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


3x*x-8*x-15=0

We add all the numbers together, and all the variables

-8x+3x*x-15=0

Wy multiply elements

3x^2-8x-15=0

a = 3; b = -8; c = -15;
Δ = b2-4ac
Δ = -82-4·3·(-15)
Δ = 244
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:

$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{61}}{2*3}=\frac{8-2\sqrt{61}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{61}}{2*3}=\frac{8+2\sqrt{61}}{6}
$