1/2a+3a=20

Solution for 1/2a+3a=20 equation:

1/2a+3a=20

We move all terms to the left:

1/2a+3a-(20)=0


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R


We add all the numbers together, and all the variables

3a+1/2a-20=0

We multiply all the terms by the denominator


3a*2a-20*2a+1=0

Wy multiply elements

6a^2-40a+1=0

a = 6; b = -40; c = +1;
Δ = b2-4ac
Δ = -402-4·6·1
Δ = 1576
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:

$\sqrt{\Delta}=\sqrt{1576}=\sqrt{4*394}=\sqrt{4}*\sqrt{394}=2\sqrt{394}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-2\sqrt{394}}{2*6}=\frac{40-2\sqrt{394}}{12}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+2\sqrt{394}}{2*6}=\frac{40+2\sqrt{394}}{12}
$