60+1/4x=X

Solution for 60+1/4x=X equation:

60+1/4x=x

We move all terms to the left:

60+1/4x-(x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+1/4x+60=0

We multiply all the terms by the denominator


-1x*4x+60*4x+1=0

Wy multiply elements

-4x^2+240x+1=0

a = -4; b = 240; c = +1;
Δ = b2-4ac
Δ = 2402-4·(-4)·1
Δ = 57616
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:

$\sqrt{\Delta}=\sqrt{57616}=\sqrt{16*3601}=\sqrt{16}*\sqrt{3601}=4\sqrt{3601}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(240)-4\sqrt{3601}}{2*-4}=\frac{-240-4\sqrt{3601}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(240)+4\sqrt{3601}}{2*-4}=\frac{-240+4\sqrt{3601}}{-8}
$