4x-8+1/4x=189

Solution for 4x-8+1/4x=189 equation:

4x-8+1/4x=189

We move all terms to the left:

4x-8+1/4x-(189)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

4x+1/4x-197=0

We multiply all the terms by the denominator


4x*4x-197*4x+1=0

Wy multiply elements

16x^2-788x+1=0

a = 16; b = -788; c = +1;
Δ = b2-4ac
Δ = -7882-4·16·1
Δ = 620880
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:

$\sqrt{\Delta}=\sqrt{620880}=\sqrt{16*38805}=\sqrt{16}*\sqrt{38805}=4\sqrt{38805}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-788)-4\sqrt{38805}}{2*16}=\frac{788-4\sqrt{38805}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-788)+4\sqrt{38805}}{2*16}=\frac{788+4\sqrt{38805}}{32}
$