2x^2-7=209

Solution for 2x^2-7=209 equation:

2x^2-7=209

We move all terms to the left:

2x^2-7-(209)=0

We add all the numbers together, and all the variables

2x^2-216=0

a = 2; b = 0; c = -216;
Δ = b2-4ac
Δ = 02-4·2·(-216)
Δ = 1728
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:

$\sqrt{\Delta}=\sqrt{1728}=\sqrt{576*3}=\sqrt{576}*\sqrt{3}=24\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{3}}{2*2}=\frac{0-24\sqrt{3}}{4}
=-\frac{24\sqrt{3}}{4}
=-6\sqrt{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{3}}{2*2}=\frac{0+24\sqrt{3}}{4}
=\frac{24\sqrt{3}}{4}
=6\sqrt{3}
$