15/x+4=3x

Solution for 15/x+4=3x equation:

15/x+4=3x

We move all terms to the left:

15/x+4-(3x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-3x+15/x+4=0

We multiply all the terms by the denominator


-3x*x+4*x+15=0

We add all the numbers together, and all the variables

4x-3x*x+15=0

Wy multiply elements

-3x^2+4x+15=0

a = -3; b = 4; c = +15;
Δ = b2-4ac
Δ = 42-4·(-3)·15
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-14}{2*-3}=\frac{-18}{-6}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+14}{2*-3}=\frac{10}{-6}
=-1+2/3
$