8x^2+9=64

Solution for 8x^2+9=64 equation:

8x^2+9=64

We move all terms to the left:

8x^2+9-(64)=0

We add all the numbers together, and all the variables

8x^2-55=0

a = 8; b = 0; c = -55;
Δ = b2-4ac
Δ = 02-4·8·(-55)
Δ = 1760
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:

$\sqrt{\Delta}=\sqrt{1760}=\sqrt{16*110}=\sqrt{16}*\sqrt{110}=4\sqrt{110}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{110}}{2*8}=\frac{0-4\sqrt{110}}{16}
=-\frac{4\sqrt{110}}{16}
=-\frac{\sqrt{110}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{110}}{2*8}=\frac{0+4\sqrt{110}}{16}
=\frac{4\sqrt{110}}{16}
=\frac{\sqrt{110}}{4}
$