-5x^2+1=-24

Solution for -5x^2+1=-24 equation:

-5x^2+1=-24

We move all terms to the left:

-5x^2+1-(-24)=0

We add all the numbers together, and all the variables

-5x^2+25=0

a = -5; b = 0; c = +25;
Δ = b2-4ac
Δ = 02-4·(-5)·25
Δ = 500
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:

$\sqrt{\Delta}=\sqrt{500}=\sqrt{100*5}=\sqrt{100}*\sqrt{5}=10\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{5}}{2*-5}=\frac{0-10\sqrt{5}}{-10}
=-\frac{10\sqrt{5}}{-10}
=-\frac{\sqrt{5}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{5}}{2*-5}=\frac{0+10\sqrt{5}}{-10}
=\frac{10\sqrt{5}}{-10}
=\frac{\sqrt{5}}{-1}
$