4x^2-49^2=15

Solution for 4x^2-49^2=15 equation:

4x^2-49^2=15

We move all terms to the left:

4x^2-49^2-(15)=0

determiningTheFunctionDomain
4x^2-15-49^2=0

We add all the numbers together, and all the variables

4x^2-2416=0

a = 4; b = 0; c = -2416;
Δ = b2-4ac
Δ = 02-4·4·(-2416)
Δ = 38656
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:

$\sqrt{\Delta}=\sqrt{38656}=\sqrt{256*151}=\sqrt{256}*\sqrt{151}=16\sqrt{151}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{151}}{2*4}=\frac{0-16\sqrt{151}}{8}
=-\frac{16\sqrt{151}}{8}
=-2\sqrt{151}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{151}}{2*4}=\frac{0+16\sqrt{151}}{8}
=\frac{16\sqrt{151}}{8}
=2\sqrt{151}
$