2-2x^2=-34

Solution for 2-2x^2=-34 equation:

2-2x^2=-34

We move all terms to the left:

2-2x^2-(-34)=0

We add all the numbers together, and all the variables

-2x^2+36=0

a = -2; b = 0; c = +36;
Δ = b2-4ac
Δ = 02-4·(-2)·36
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{2}}{2*-2}=\frac{0-12\sqrt{2}}{-4}
=-\frac{12\sqrt{2}}{-4}
=-\frac{3\sqrt{2}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{2}}{2*-2}=\frac{0+12\sqrt{2}}{-4}
=\frac{12\sqrt{2}}{-4}
=\frac{3\sqrt{2}}{-1}
$