8x^2-3=509

Solution for 8x^2-3=509 equation:

8x^2-3=509

We move all terms to the left:

8x^2-3-(509)=0

We add all the numbers together, and all the variables

8x^2-512=0

a = 8; b = 0; c = -512;
Δ = b2-4ac
Δ = 02-4·8·(-512)
Δ = 16384
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16384}=128$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-128}{2*8}=\frac{-128}{16}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+128}{2*8}=\frac{128}{16}
=8
$