9-2x^2=-17

Solution for 9-2x^2=-17 equation:

9-2x^2=-17

We move all terms to the left:

9-2x^2-(-17)=0

We add all the numbers together, and all the variables

-2x^2+26=0

a = -2; b = 0; c = +26;
Δ = b2-4ac
Δ = 02-4·(-2)·26
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{13}}{2*-2}=\frac{0-4\sqrt{13}}{-4}
=-\frac{4\sqrt{13}}{-4}
=-\frac{\sqrt{13}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{13}}{2*-2}=\frac{0+4\sqrt{13}}{-4}
=\frac{4\sqrt{13}}{-4}
=\frac{\sqrt{13}}{-1}
$