(2/3)a+1=16a

Solution for (2/3)a+1=16a equation:

(2/3)a+1=16a

We move all terms to the left:

(2/3)a+1-(16a)=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

(+2/3)a-16a+1=0

We add all the numbers together, and all the variables

-16a+(+2/3)a+1=0

We multiply parentheses

2a^2-16a+1=0

a = 2; b = -16; c = +1;
Δ = b2-4ac
Δ = -162-4·2·1
Δ = 248
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:

$\sqrt{\Delta}=\sqrt{248}=\sqrt{4*62}=\sqrt{4}*\sqrt{62}=2\sqrt{62}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{62}}{2*2}=\frac{16-2\sqrt{62}}{4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{62}}{2*2}=\frac{16+2\sqrt{62}}{4}
$