25x^2-6=2

Solution for 25x^2-6=2 equation:

25x^2-6=2

We move all terms to the left:

25x^2-6-(2)=0

We add all the numbers together, and all the variables

25x^2-8=0

a = 25; b = 0; c = -8;
Δ = b2-4ac
Δ = 02-4·25·(-8)
Δ = 800
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:

$\sqrt{\Delta}=\sqrt{800}=\sqrt{400*2}=\sqrt{400}*\sqrt{2}=20\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{2}}{2*25}=\frac{0-20\sqrt{2}}{50}
=-\frac{20\sqrt{2}}{50}
=-\frac{2\sqrt{2}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{2}}{2*25}=\frac{0+20\sqrt{2}}{50}
=\frac{20\sqrt{2}}{50}
=\frac{2\sqrt{2}}{5}
$