76=384/x+2x

Solution for 76=384/x+2x equation:

76=384/x+2x

We move all terms to the left:

76-(384/x+2x)=0


Domain of the equation: x+2x)!=0

x∈R


We add all the numbers together, and all the variables

-(+2x+384/x)+76=0

We get rid of parentheses

-2x-384/x+76=0

We multiply all the terms by the denominator


-2x*x+76*x-384=0

We add all the numbers together, and all the variables

76x-2x*x-384=0

Wy multiply elements

-2x^2+76x-384=0

a = -2; b = 76; c = -384;
Δ = b2-4ac
Δ = 762-4·(-2)·(-384)
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(76)-52}{2*-2}=\frac{-128}{-4}
=+32
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(76)+52}{2*-2}=\frac{-24}{-4}
=+6
$