48/x+10+3x=10+6x

Solution for 48/x+10+3x=10+6x equation:

48/x+10+3x=10+6x

We move all terms to the left:

48/x+10+3x-(10+6x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

48/x+3x-(6x+10)+10=0

We add all the numbers together, and all the variables

3x+48/x-(6x+10)+10=0

We get rid of parentheses

3x+48/x-6x-10+10=0

We multiply all the terms by the denominator


3x*x-6x*x-10*x+10*x+48=0

We add all the numbers together, and all the variables

3x*x-6x*x+48=0

Wy multiply elements

3x^2-6x^2+48=0

We add all the numbers together, and all the variables

-3x^2+48=0

a = -3; b = 0; c = +48;
Δ = b2-4ac
Δ = 02-4·(-3)·48
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24}{2*-3}=\frac{-24}{-6}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24}{2*-3}=\frac{24}{-6}
=-4
$