48x^2-65=38

Solution for 48x^2-65=38 equation:

48x^2-65=38

We move all terms to the left:

48x^2-65-(38)=0

We add all the numbers together, and all the variables

48x^2-103=0

a = 48; b = 0; c = -103;
Δ = b2-4ac
Δ = 02-4·48·(-103)
Δ = 19776
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:

$\sqrt{\Delta}=\sqrt{19776}=\sqrt{64*309}=\sqrt{64}*\sqrt{309}=8\sqrt{309}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{309}}{2*48}=\frac{0-8\sqrt{309}}{96}
=-\frac{8\sqrt{309}}{96}
=-\frac{\sqrt{309}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{309}}{2*48}=\frac{0+8\sqrt{309}}{96}
=\frac{8\sqrt{309}}{96}
=\frac{\sqrt{309}}{12}
$