(2/3a)+a=600

Solution for (2/3a)+a=600 equation:

(2/3a)+a=600

We move all terms to the left:

(2/3a)+a-(600)=0


Domain of the equation: 3a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

(+2/3a)+a-600=0

We add all the numbers together, and all the variables

a+(+2/3a)-600=0

We get rid of parentheses

a+2/3a-600=0

We multiply all the terms by the denominator


a*3a-600*3a+2=0

Wy multiply elements

3a^2-1800a+2=0

a = 3; b = -1800; c = +2;
Δ = b2-4ac
Δ = -18002-4·3·2
Δ = 3239976
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:

$\sqrt{\Delta}=\sqrt{3239976}=\sqrt{4*809994}=\sqrt{4}*\sqrt{809994}=2\sqrt{809994}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1800)-2\sqrt{809994}}{2*3}=\frac{1800-2\sqrt{809994}}{6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1800)+2\sqrt{809994}}{2*3}=\frac{1800+2\sqrt{809994}}{6}
$