x^2=14x+1/48

Solution for x^2=14x+1/48 equation:

x^2=14x+1/48

We move all terms to the left:

x^2-(14x+1/48)=0

We add all the numbers together, and all the variables

x^2-(+14x+1/48)=0

We get rid of parentheses

x^2-14x-1/48=0

We multiply all the terms by the denominator


x^2*48-14x*48-1=0

Wy multiply elements

48x^2-672x-1=0

a = 48; b = -672; c = -1;
Δ = b2-4ac
Δ = -6722-4·48·(-1)
Δ = 451776
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:

$\sqrt{\Delta}=\sqrt{451776}=\sqrt{64*7059}=\sqrt{64}*\sqrt{7059}=8\sqrt{7059}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-672)-8\sqrt{7059}}{2*48}=\frac{672-8\sqrt{7059}}{96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-672)+8\sqrt{7059}}{2*48}=\frac{672+8\sqrt{7059}}{96}
$