64x^2-24=30

Solution for 64x^2-24=30 equation:

64x^2-24=30

We move all terms to the left:

64x^2-24-(30)=0

We add all the numbers together, and all the variables

64x^2-54=0

a = 64; b = 0; c = -54;
Δ = b2-4ac
Δ = 02-4·64·(-54)
Δ = 13824
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:

$\sqrt{\Delta}=\sqrt{13824}=\sqrt{2304*6}=\sqrt{2304}*\sqrt{6}=48\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-48\sqrt{6}}{2*64}=\frac{0-48\sqrt{6}}{128}
=-\frac{48\sqrt{6}}{128}
=-\frac{3\sqrt{6}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+48\sqrt{6}}{2*64}=\frac{0+48\sqrt{6}}{128}
=\frac{48\sqrt{6}}{128}
=\frac{3\sqrt{6}}{8}
$