32x^2=39

Solution for 32x^2=39 equation:

32x^2=39

We move all terms to the left:

32x^2-(39)=0

a = 32; b = 0; c = -39;
Δ = b2-4ac
Δ = 02-4·32·(-39)
Δ = 4992
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:

$\sqrt{\Delta}=\sqrt{4992}=\sqrt{64*78}=\sqrt{64}*\sqrt{78}=8\sqrt{78}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{78}}{2*32}=\frac{0-8\sqrt{78}}{64}
=-\frac{8\sqrt{78}}{64}
=-\frac{\sqrt{78}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{78}}{2*32}=\frac{0+8\sqrt{78}}{64}
=\frac{8\sqrt{78}}{64}
=\frac{\sqrt{78}}{8}
$