48x^2-x^2-9=0

Solution for 48x^2-x^2-9=0 equation:

48x^2-x^2-9=0

We add all the numbers together, and all the variables

47x^2-9=0

a = 47; b = 0; c = -9;
Δ = b2-4ac
Δ = 02-4·47·(-9)
Δ = 1692
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:

$\sqrt{\Delta}=\sqrt{1692}=\sqrt{36*47}=\sqrt{36}*\sqrt{47}=6\sqrt{47}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{47}}{2*47}=\frac{0-6\sqrt{47}}{94}
=-\frac{6\sqrt{47}}{94}
=-\frac{3\sqrt{47}}{47}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{47}}{2*47}=\frac{0+6\sqrt{47}}{94}
=\frac{6\sqrt{47}}{94}
=\frac{3\sqrt{47}}{47}
$