76=3x+6/x

Solution for 76=3x+6/x equation:

76=3x+6/x

We move all terms to the left:

76-(3x+6/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(+3x+6/x)+76=0

We get rid of parentheses

-3x-6/x+76=0

We multiply all the terms by the denominator


-3x*x+76*x-6=0

We add all the numbers together, and all the variables

76x-3x*x-6=0

Wy multiply elements

-3x^2+76x-6=0

a = -3; b = 76; c = -6;
Δ = b2-4ac
Δ = 762-4·(-3)·(-6)
Δ = 5704
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:

$\sqrt{\Delta}=\sqrt{5704}=\sqrt{4*1426}=\sqrt{4}*\sqrt{1426}=2\sqrt{1426}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(76)-2\sqrt{1426}}{2*-3}=\frac{-76-2\sqrt{1426}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(76)+2\sqrt{1426}}{2*-3}=\frac{-76+2\sqrt{1426}}{-6}
$