10-2x^2=-64

Solution for 10-2x^2=-64 equation:

10-2x^2=-64

We move all terms to the left:

10-2x^2-(-64)=0

We add all the numbers together, and all the variables

-2x^2+74=0

a = -2; b = 0; c = +74;
Δ = b2-4ac
Δ = 02-4·(-2)·74
Δ = 592
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:

$\sqrt{\Delta}=\sqrt{592}=\sqrt{16*37}=\sqrt{16}*\sqrt{37}=4\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{37}}{2*-2}=\frac{0-4\sqrt{37}}{-4}
=-\frac{4\sqrt{37}}{-4}
=-\frac{\sqrt{37}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{37}}{2*-2}=\frac{0+4\sqrt{37}}{-4}
=\frac{4\sqrt{37}}{-4}
=\frac{\sqrt{37}}{-1}
$