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

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

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

We move all terms to the left:

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


Domain of the equation: 3)a!=0

a!=0/1

a!=0

a∈R



Domain of the equation: 2)a!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

a^2+a^2-30=0

We add all the numbers together, and all the variables

2a^2-30=0

a = 2; b = 0; c = -30;
Δ = b2-4ac
Δ = 02-4·2·(-30)
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{15}}{2*2}=\frac{0-4\sqrt{15}}{4}
=-\frac{4\sqrt{15}}{4}
=-\sqrt{15}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{15}}{2*2}=\frac{0+4\sqrt{15}}{4}
=\frac{4\sqrt{15}}{4}
=\sqrt{15}
$