-3-10x^2=-53

Solution for -3-10x^2=-53 equation:

-3-10x^2=-53

We move all terms to the left:

-3-10x^2-(-53)=0

We add all the numbers together, and all the variables

-10x^2+50=0

a = -10; b = 0; c = +50;
Δ = b2-4ac
Δ = 02-4·(-10)·50
Δ = 2000
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:

$\sqrt{\Delta}=\sqrt{2000}=\sqrt{400*5}=\sqrt{400}*\sqrt{5}=20\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{5}}{2*-10}=\frac{0-20\sqrt{5}}{-20}
=-\frac{20\sqrt{5}}{-20}
=-\frac{\sqrt{5}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{5}}{2*-10}=\frac{0+20\sqrt{5}}{-20}
=\frac{20\sqrt{5}}{-20}
=\frac{\sqrt{5}}{-1}
$