2x-1/4x=9

Solution for 2x-1/4x=9 equation:

2x-1/4x=9

We move all terms to the left:

2x-1/4x-(9)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


2x*4x-9*4x-1=0

Wy multiply elements

8x^2-36x-1=0

a = 8; b = -36; c = -1;
Δ = b2-4ac
Δ = -362-4·8·(-1)
Δ = 1328
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:

$\sqrt{\Delta}=\sqrt{1328}=\sqrt{16*83}=\sqrt{16}*\sqrt{83}=4\sqrt{83}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{83}}{2*8}=\frac{36-4\sqrt{83}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{83}}{2*8}=\frac{36+4\sqrt{83}}{16}
$