80=2x+4/3x

Solution for 80=2x+4/3x equation:

80=2x+4/3x

We move all terms to the left:

80-(2x+4/3x)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(+2x+4/3x)+80=0

We get rid of parentheses

-2x-4/3x+80=0

We multiply all the terms by the denominator


-2x*3x+80*3x-4=0

Wy multiply elements

-6x^2+240x-4=0

a = -6; b = 240; c = -4;
Δ = b2-4ac
Δ = 2402-4·(-6)·(-4)
Δ = 57504
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:

$\sqrt{\Delta}=\sqrt{57504}=\sqrt{16*3594}=\sqrt{16}*\sqrt{3594}=4\sqrt{3594}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(240)-4\sqrt{3594}}{2*-6}=\frac{-240-4\sqrt{3594}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(240)+4\sqrt{3594}}{2*-6}=\frac{-240+4\sqrt{3594}}{-12}
$