1/4x-x=48

Solution for 1/4x-x=48 equation:

1/4x-x=48

We move all terms to the left:

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

We multiply all the terms by the denominator


-1x*4x-48*4x+1=0

Wy multiply elements

-4x^2-192x+1=0

a = -4; b = -192; c = +1;
Δ = b2-4ac
Δ = -1922-4·(-4)·1
Δ = 36880
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:

$\sqrt{\Delta}=\sqrt{36880}=\sqrt{16*2305}=\sqrt{16}*\sqrt{2305}=4\sqrt{2305}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-192)-4\sqrt{2305}}{2*-4}=\frac{192-4\sqrt{2305}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-192)+4\sqrt{2305}}{2*-4}=\frac{192+4\sqrt{2305}}{-8}
$