2x2-25=97

Solution for 2x2-25=97 equation:

2x^2-25=97

We move all terms to the left:

2x^2-25-(97)=0

We add all the numbers together, and all the variables

2x^2-122=0

a = 2; b = 0; c = -122;
Δ = b2-4ac
Δ = 02-4·2·(-122)
Δ = 976
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:

$\sqrt{\Delta}=\sqrt{976}=\sqrt{16*61}=\sqrt{16}*\sqrt{61}=4\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{61}}{2*2}=\frac{0-4\sqrt{61}}{4}
=-\frac{4\sqrt{61}}{4}
=-\sqrt{61}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{61}}{2*2}=\frac{0+4\sqrt{61}}{4}
=\frac{4\sqrt{61}}{4}
=\sqrt{61}
$