8x^2+9=313

Solution for 8x^2+9=313 equation:

8x^2+9=313

We move all terms to the left:

8x^2+9-(313)=0

We add all the numbers together, and all the variables

8x^2-304=0

a = 8; b = 0; c = -304;
Δ = b2-4ac
Δ = 02-4·8·(-304)
Δ = 9728
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:

$\sqrt{\Delta}=\sqrt{9728}=\sqrt{256*38}=\sqrt{256}*\sqrt{38}=16\sqrt{38}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{38}}{2*8}=\frac{0-16\sqrt{38}}{16}
=-\frac{16\sqrt{38}}{16}
=-\sqrt{38}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{38}}{2*8}=\frac{0+16\sqrt{38}}{16}
=\frac{16\sqrt{38}}{16}
=\sqrt{38}
$