48x2+9=50

Solution for 48x2+9=50 equation:

48x^2+9=50

We move all terms to the left:

48x^2+9-(50)=0

We add all the numbers together, and all the variables

48x^2-41=0

a = 48; b = 0; c = -41;
Δ = b2-4ac
Δ = 02-4·48·(-41)
Δ = 7872
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:

$\sqrt{\Delta}=\sqrt{7872}=\sqrt{64*123}=\sqrt{64}*\sqrt{123}=8\sqrt{123}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{123}}{2*48}=\frac{0-8\sqrt{123}}{96}
=-\frac{8\sqrt{123}}{96}
=-\frac{\sqrt{123}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{123}}{2*48}=\frac{0+8\sqrt{123}}{96}
=\frac{8\sqrt{123}}{96}
=\frac{\sqrt{123}}{12}
$