a^2=64/224

Solution for a^2=64/224 equation:

a^2=64/224

We move all terms to the left:

a^2-(64/224)=0

We add all the numbers together, and all the variables

a^2-(+64/224)=0

We get rid of parentheses

a^2-64/224=0

We multiply all the terms by the denominator


a^2*224-64=0

Wy multiply elements

224a^2-64=0

a = 224; b = 0; c = -64;
Δ = b2-4ac
Δ = 02-4·224·(-64)
Δ = 57344
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:

$\sqrt{\Delta}=\sqrt{57344}=\sqrt{4096*14}=\sqrt{4096}*\sqrt{14}=64\sqrt{14}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-64\sqrt{14}}{2*224}=\frac{0-64\sqrt{14}}{448}
=-\frac{64\sqrt{14}}{448}
=-\frac{\sqrt{14}}{7}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+64\sqrt{14}}{2*224}=\frac{0+64\sqrt{14}}{448}
=\frac{64\sqrt{14}}{448}
=\frac{\sqrt{14}}{7}
$