1/2x-8=20x=

Solution for 1/2x-8=20x= equation:

1/2x-8=20x=

We move all terms to the left:

1/2x-8-(20x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-20x+1/2x-8=0

We multiply all the terms by the denominator


-20x*2x-8*2x+1=0

Wy multiply elements

-40x^2-16x+1=0

a = -40; b = -16; c = +1;
Δ = b2-4ac
Δ = -162-4·(-40)·1
Δ = 416
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:

$\sqrt{\Delta}=\sqrt{416}=\sqrt{16*26}=\sqrt{16}*\sqrt{26}=4\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{26}}{2*-40}=\frac{16-4\sqrt{26}}{-80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{26}}{2*-40}=\frac{16+4\sqrt{26}}{-80}
$