(4/11)a+(16/121)a+(64/1331)a=768

Solution for (4/11)a+(16/121)a+(64/1331)a=768 equation:

(4/11)a+(16/121)a+(64/1331)a=768

We move all terms to the left:

(4/11)a+(16/121)a+(64/1331)a-(768)=0


Domain of the equation: 11)a!=0

a!=0/1

a!=0

a∈R



Domain of the equation: 121)a!=0

a!=0/1

a!=0

a∈R



Domain of the equation: 1331)a!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

(+4/11)a+(+16/121)a+(+64/1331)a-768=0

We multiply parentheses

4a^2+16a^2+64a^2-768=0

We add all the numbers together, and all the variables

84a^2-768=0

a = 84; b = 0; c = -768;
Δ = b2-4ac
Δ = 02-4·84·(-768)
Δ = 258048
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:

$\sqrt{\Delta}=\sqrt{258048}=\sqrt{36864*7}=\sqrt{36864}*\sqrt{7}=192\sqrt{7}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-192\sqrt{7}}{2*84}=\frac{0-192\sqrt{7}}{168}
=-\frac{192\sqrt{7}}{168}
=-\frac{8\sqrt{7}}{7}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+192\sqrt{7}}{2*84}=\frac{0+192\sqrt{7}}{168}
=\frac{192\sqrt{7}}{168}
=\frac{8\sqrt{7}}{7}
$