27-5x^2=-53

Solution for 27-5x^2=-53 equation:

27-5x^2=-53

We move all terms to the left:

27-5x^2-(-53)=0

We add all the numbers together, and all the variables

-5x^2+80=0

a = -5; b = 0; c = +80;
Δ = b2-4ac
Δ = 02-4·(-5)·80
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40}{2*-5}=\frac{-40}{-10}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40}{2*-5}=\frac{40}{-10}
=-4
$