x(1/4)=15/48

Solution for x(1/4)=15/48 equation:

x(1/4)=15/48

We move all terms to the left:

x(1/4)-(15/48)=0

We add all the numbers together, and all the variables

x(+1/4)-(+15/48)=0

We multiply parentheses

x^2-(+15/48)=0

We get rid of parentheses

x^2-15/48=0

We multiply all the terms by the denominator


x^2*48-15=0

Wy multiply elements

48x^2-15=0

a = 48; b = 0; c = -15;
Δ = b2-4ac
Δ = 02-4·48·(-15)
Δ = 2880
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:

$\sqrt{\Delta}=\sqrt{2880}=\sqrt{576*5}=\sqrt{576}*\sqrt{5}=24\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{5}}{2*48}=\frac{0-24\sqrt{5}}{96}
=-\frac{24\sqrt{5}}{96}
=-\frac{\sqrt{5}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{5}}{2*48}=\frac{0+24\sqrt{5}}{96}
=\frac{24\sqrt{5}}{96}
=\frac{\sqrt{5}}{4}
$