2x-1/4x=21

Solution for 2x-1/4x=21 equation:

2x-1/4x=21

We move all terms to the left:

2x-1/4x-(21)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


2x*4x-21*4x-1=0

Wy multiply elements

8x^2-84x-1=0

a = 8; b = -84; c = -1;
Δ = b2-4ac
Δ = -842-4·8·(-1)
Δ = 7088
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:

$\sqrt{\Delta}=\sqrt{7088}=\sqrt{16*443}=\sqrt{16}*\sqrt{443}=4\sqrt{443}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-4\sqrt{443}}{2*8}=\frac{84-4\sqrt{443}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+4\sqrt{443}}{2*8}=\frac{84+4\sqrt{443}}{16}
$