1/4+x2-16=0

Solution for 1/4+x2-16=0 equation:

1/4+x2-16=0

We add all the numbers together, and all the variables

x^2-16+1/4=0

We multiply all the terms by the denominator


x^2*4+1-16*4=0

We add all the numbers together, and all the variables

x^2*4-63=0

Wy multiply elements

4x^2-63=0

a = 4; b = 0; c = -63;
Δ = b2-4ac
Δ = 02-4·4·(-63)
Δ = 1008
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:

$\sqrt{\Delta}=\sqrt{1008}=\sqrt{144*7}=\sqrt{144}*\sqrt{7}=12\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{7}}{2*4}=\frac{0-12\sqrt{7}}{8}
=-\frac{12\sqrt{7}}{8}
=-\frac{3\sqrt{7}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{7}}{2*4}=\frac{0+12\sqrt{7}}{8}
=\frac{12\sqrt{7}}{8}
=\frac{3\sqrt{7}}{2}
$