330=2l+2/3l

Solution for 330=2l+2/3l equation:

330=2l+2/3l

We move all terms to the left:

330-(2l+2/3l)=0


Domain of the equation: 3l)!=0

l!=0/1

l!=0

l∈R


We add all the numbers together, and all the variables

-(+2l+2/3l)+330=0

We get rid of parentheses

-2l-2/3l+330=0

We multiply all the terms by the denominator


-2l*3l+330*3l-2=0

Wy multiply elements

-6l^2+990l-2=0

a = -6; b = 990; c = -2;
Δ = b2-4ac
Δ = 9902-4·(-6)·(-2)
Δ = 980052
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$l_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$l_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{980052}=\sqrt{4*245013}=\sqrt{4}*\sqrt{245013}=2\sqrt{245013}$
$l_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(990)-2\sqrt{245013}}{2*-6}=\frac{-990-2\sqrt{245013}}{-12}
$
$l_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(990)+2\sqrt{245013}}{2*-6}=\frac{-990+2\sqrt{245013}}{-12}
$