2a+2/3a+2/3a=320

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Solution for 2a+2/3a+2/3a=320 equation: 



2a+2/3a+2/3a=320

We move all terms to the left:

2a+2/3a+2/3a-(320)=0



Domain of the equation: 3a!=0

a!=0/3

a!=0

a∈R



We multiply all the terms by the denominator


2a*3a-320*3a+2+2=0

We add all the numbers together, and all the variables

2a*3a-320*3a+4=0

Wy multiply elements

6a^2-960a+4=0

a = 6; b = -960; c = +4;
Δ = b2-4ac
Δ = -9602-4·6·4
Δ = 921504
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:


$\sqrt{\Delta}=\sqrt{921504}=\sqrt{16*57594}=\sqrt{16}*\sqrt{57594}=4\sqrt{57594}$


$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-960)-4\sqrt{57594}}{2*6}=\frac{960-4\sqrt{57594}}{12}
$


$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-960)+4\sqrt{57594}}{2*6}=\frac{960+4\sqrt{57594}}{12}
$

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