9x^2-40x^2+1=0

Solution for 9x^2-40x^2+1=0 equation:

9x^2-40x^2+1=0

We add all the numbers together, and all the variables

-31x^2+1=0

a = -31; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-31)·1
Δ = 124
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:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{31}}{2*-31}=\frac{0-2\sqrt{31}}{-62}
=-\frac{2\sqrt{31}}{-62}
=-\frac{\sqrt{31}}{-31}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{31}}{2*-31}=\frac{0+2\sqrt{31}}{-62}
=\frac{2\sqrt{31}}{-62}
=\frac{\sqrt{31}}{-31}
$