27-2x^2=-53

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

27-2x^2=-53

We move all terms to the left:

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

We add all the numbers together, and all the variables

-2x^2+80=0

a = -2; b = 0; c = +80;
Δ = b2-4ac
Δ = 02-4·(-2)·80
Δ = 640
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:

$\sqrt{\Delta}=\sqrt{640}=\sqrt{64*10}=\sqrt{64}*\sqrt{10}=8\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{10}}{2*-2}=\frac{0-8\sqrt{10}}{-4}
=-\frac{8\sqrt{10}}{-4}
=-\frac{2\sqrt{10}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{10}}{2*-2}=\frac{0+8\sqrt{10}}{-4}
=\frac{8\sqrt{10}}{-4}
=\frac{2\sqrt{10}}{-1}
$