1/4x-5x=28

Solution for 1/4x-5x=28 equation:

1/4x-5x=28

We move all terms to the left:

1/4x-5x-(28)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

-5x+1/4x-28=0

We multiply all the terms by the denominator


-5x*4x-28*4x+1=0

Wy multiply elements

-20x^2-112x+1=0

a = -20; b = -112; c = +1;
Δ = b2-4ac
Δ = -1122-4·(-20)·1
Δ = 12624
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:

$\sqrt{\Delta}=\sqrt{12624}=\sqrt{16*789}=\sqrt{16}*\sqrt{789}=4\sqrt{789}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-112)-4\sqrt{789}}{2*-20}=\frac{112-4\sqrt{789}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-112)+4\sqrt{789}}{2*-20}=\frac{112+4\sqrt{789}}{-40}
$