8(-2)+2+2x^2=180

Solution for 8(-2)+2+2x^2=180 equation:

8(-2)+2+2x^2=180

We move all terms to the left:

8(-2)+2+2x^2-(180)=0

determiningTheFunctionDomain
2x^2+2-180+8(-2)=0

We add all the numbers together, and all the variables

2x^2-194=0

a = 2; b = 0; c = -194;
Δ = b2-4ac
Δ = 02-4·2·(-194)
Δ = 1552
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:

$\sqrt{\Delta}=\sqrt{1552}=\sqrt{16*97}=\sqrt{16}*\sqrt{97}=4\sqrt{97}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{97}}{2*2}=\frac{0-4\sqrt{97}}{4}
=-\frac{4\sqrt{97}}{4}
=-\sqrt{97}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{97}}{2*2}=\frac{0+4\sqrt{97}}{4}
=\frac{4\sqrt{97}}{4}
=\sqrt{97}
$