2x^2-9=121

Solution for 2x^2-9=121 equation:

2x^2-9=121

We move all terms to the left:

2x^2-9-(121)=0

We add all the numbers together, and all the variables

2x^2-130=0

a = 2; b = 0; c = -130;
Δ = b2-4ac
Δ = 02-4·2·(-130)
Δ = 1040
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:

$\sqrt{\Delta}=\sqrt{1040}=\sqrt{16*65}=\sqrt{16}*\sqrt{65}=4\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{65}}{2*2}=\frac{0-4\sqrt{65}}{4}
=-\frac{4\sqrt{65}}{4}
=-\sqrt{65}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{65}}{2*2}=\frac{0+4\sqrt{65}}{4}
=\frac{4\sqrt{65}}{4}
=\sqrt{65}
$