-5x^2-8x^2=-1

Solution for -5x^2-8x^2=-1 equation:

-5x^2-8x^2=-1

We move all terms to the left:

-5x^2-8x^2-(-1)=0

We add all the numbers together, and all the variables

-13x^2+1=0

a = -13; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-13)·1
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{13}}{2*-13}=\frac{0-2\sqrt{13}}{-26}
=-\frac{2\sqrt{13}}{-26}
=-\frac{\sqrt{13}}{-13}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{13}}{2*-13}=\frac{0+2\sqrt{13}}{-26}
=\frac{2\sqrt{13}}{-26}
=\frac{\sqrt{13}}{-13}
$