10x^2-1=269

Solution for 10x^2-1=269 equation:

10x^2-1=269

We move all terms to the left:

10x^2-1-(269)=0

We add all the numbers together, and all the variables

10x^2-270=0

a = 10; b = 0; c = -270;
Δ = b2-4ac
Δ = 02-4·10·(-270)
Δ = 10800
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:

$\sqrt{\Delta}=\sqrt{10800}=\sqrt{3600*3}=\sqrt{3600}*\sqrt{3}=60\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-60\sqrt{3}}{2*10}=\frac{0-60\sqrt{3}}{20}
=-\frac{60\sqrt{3}}{20}
=-3\sqrt{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+60\sqrt{3}}{2*10}=\frac{0+60\sqrt{3}}{20}
=\frac{60\sqrt{3}}{20}
=3\sqrt{3}
$