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

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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} $

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