8x^2+5=229

Solution for 8x^2+5=229 equation:

8x^2+5=229

We move all terms to the left:

8x^2+5-(229)=0

We add all the numbers together, and all the variables

8x^2-224=0

a = 8; b = 0; c = -224;
Δ = b2-4ac
Δ = 02-4·8·(-224)
Δ = 7168
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:

$\sqrt{\Delta}=\sqrt{7168}=\sqrt{1024*7}=\sqrt{1024}*\sqrt{7}=32\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-32\sqrt{7}}{2*8}=\frac{0-32\sqrt{7}}{16}
=-\frac{32\sqrt{7}}{16}
=-2\sqrt{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+32\sqrt{7}}{2*8}=\frac{0+32\sqrt{7}}{16}
=\frac{32\sqrt{7}}{16}
=2\sqrt{7}
$