9x^2-x^2=81

Solution for 9x^2-x^2=81 equation:

9x^2-x^2=81

We move all terms to the left:

9x^2-x^2-(81)=0

We add all the numbers together, and all the variables

8x^2-81=0

a = 8; b = 0; c = -81;
Δ = b2-4ac
Δ = 02-4·8·(-81)
Δ = 2592
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:

$\sqrt{\Delta}=\sqrt{2592}=\sqrt{1296*2}=\sqrt{1296}*\sqrt{2}=36\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-36\sqrt{2}}{2*8}=\frac{0-36\sqrt{2}}{16}
=-\frac{36\sqrt{2}}{16}
=-\frac{9\sqrt{2}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+36\sqrt{2}}{2*8}=\frac{0+36\sqrt{2}}{16}
=\frac{36\sqrt{2}}{16}
=\frac{9\sqrt{2}}{4}
$