(1/3)a+a/2=30

Solution for (1/3)a+a/2=30 equation:

(1/3)a+a/2=30

We move all terms to the left:

(1/3)a+a/2-(30)=0


Domain of the equation: 3)a!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

(+1/3)a+a/2-30=0

We multiply parentheses

a^2+a/2-30=0

We multiply all the terms by the denominator


a^2*2+a-30*2=0

We add all the numbers together, and all the variables

a^2*2+a-60=0

Wy multiply elements

2a^2+a-60=0

a = 2; b = 1; c = -60;
Δ = b2-4ac
Δ = 12-4·2·(-60)
Δ = 481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{481}}{2*2}=\frac{-1-\sqrt{481}}{4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{481}}{2*2}=\frac{-1+\sqrt{481}}{4}
$