8x2+2/3=81

Solution for 8x2+2/3=81 equation:

8x^2+2/3=81

We move all terms to the left:

8x^2+2/3-(81)=0

determiningTheFunctionDomain
8x^2-81+2/3=0

We multiply all the terms by the denominator


8x^2*3+2-81*3=0

We add all the numbers together, and all the variables

8x^2*3-241=0

Wy multiply elements

24x^2-241=0

a = 24; b = 0; c = -241;
Δ = b2-4ac
Δ = 02-4·24·(-241)
Δ = 23136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{23136}=\sqrt{16*1446}=\sqrt{16}*\sqrt{1446}=4\sqrt{1446}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{1446}}{2*24}=\frac{0-4\sqrt{1446}}{48}
=-\frac{4\sqrt{1446}}{48}
=-\frac{\sqrt{1446}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{1446}}{2*24}=\frac{0+4\sqrt{1446}}{48}
=\frac{4\sqrt{1446}}{48}
=\frac{\sqrt{1446}}{12}
$