1/3a+22=2a

Solution for 1/3a+22=2a equation:

1/3a+22=2a

We move all terms to the left:

1/3a+22-(2a)=0


Domain of the equation: 3a!=0

a!=0/3

a!=0

a∈R


We add all the numbers together, and all the variables

-2a+1/3a+22=0

We multiply all the terms by the denominator


-2a*3a+22*3a+1=0

Wy multiply elements

-6a^2+66a+1=0

a = -6; b = 66; c = +1;
Δ = b2-4ac
Δ = 662-4·(-6)·1
Δ = 4380
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:

$\sqrt{\Delta}=\sqrt{4380}=\sqrt{4*1095}=\sqrt{4}*\sqrt{1095}=2\sqrt{1095}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(66)-2\sqrt{1095}}{2*-6}=\frac{-66-2\sqrt{1095}}{-12}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(66)+2\sqrt{1095}}{2*-6}=\frac{-66+2\sqrt{1095}}{-12}
$