3x+3/x=15

Solution for 3x+3/x=15 equation:

3x+3/x=15

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

3x^2-15x+3=0

a = 3; b = -15; c = +3;
Δ = b2-4ac
Δ = -152-4·3·3
Δ = 189
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:

$\sqrt{\Delta}=\sqrt{189}=\sqrt{9*21}=\sqrt{9}*\sqrt{21}=3\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3\sqrt{21}}{2*3}=\frac{15-3\sqrt{21}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3\sqrt{21}}{2*3}=\frac{15+3\sqrt{21}}{6}
$