270=2x+4/3x

Solution for 270=2x+4/3x equation:

270=2x+4/3x

We move all terms to the left:

270-(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)+270=0

We get rid of parentheses

-2x-4/3x+270=0

We multiply all the terms by the denominator


-2x*3x+270*3x-4=0

Wy multiply elements

-6x^2+810x-4=0

a = -6; b = 810; c = -4;
Δ = b2-4ac
Δ = 8102-4·(-6)·(-4)
Δ = 656004
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:

$\sqrt{\Delta}=\sqrt{656004}=\sqrt{4*164001}=\sqrt{4}*\sqrt{164001}=2\sqrt{164001}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(810)-2\sqrt{164001}}{2*-6}=\frac{-810-2\sqrt{164001}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(810)+2\sqrt{164001}}{2*-6}=\frac{-810+2\sqrt{164001}}{-12}
$