X^2-27x^2+1=0

Solution for X^2-27x^2+1=0 equation:

X^2-27X^2+1=0

We add all the numbers together, and all the variables

-26X^2+1=0

a = -26; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-26)·1
Δ = 104
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:

$\sqrt{\Delta}=\sqrt{104}=\sqrt{4*26}=\sqrt{4}*\sqrt{26}=2\sqrt{26}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{26}}{2*-26}=\frac{0-2\sqrt{26}}{-52}
=-\frac{2\sqrt{26}}{-52}
=-\frac{\sqrt{26}}{-26}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{26}}{2*-26}=\frac{0+2\sqrt{26}}{-52}
=\frac{2\sqrt{26}}{-52}
=\frac{\sqrt{26}}{-26}
$