8x^2+x^2=81

Solution for 8x^2+x^2=81 equation:

8x^2+x^2=81

We move all terms to the left:

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

We add all the numbers together, and all the variables

9x^2-81=0

a = 9; b = 0; c = -81;
Δ = b2-4ac
Δ = 02-4·9·(-81)
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-54}{2*9}=\frac{-54}{18}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+54}{2*9}=\frac{54}{18}
=3
$