5x^2-32=-10

Solution for 5x^2-32=-10 equation:

5x^2-32=-10

We move all terms to the left:

5x^2-32-(-10)=0

We add all the numbers together, and all the variables

5x^2-22=0

a = 5; b = 0; c = -22;
Δ = b2-4ac
Δ = 02-4·5·(-22)
Δ = 440
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:

$\sqrt{\Delta}=\sqrt{440}=\sqrt{4*110}=\sqrt{4}*\sqrt{110}=2\sqrt{110}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{110}}{2*5}=\frac{0-2\sqrt{110}}{10}
=-\frac{2\sqrt{110}}{10}
=-\frac{\sqrt{110}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{110}}{2*5}=\frac{0+2\sqrt{110}}{10}
=\frac{2\sqrt{110}}{10}
=\frac{\sqrt{110}}{5}
$