(1/4)x=81x+2

Solution for (1/4)x=81x+2 equation:

(1/4)x=81x+2

We move all terms to the left:

(1/4)x-(81x+2)=0


Domain of the equation: 4)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+1/4)x-(81x+2)=0

We multiply parentheses

x^2-(81x+2)=0

We get rid of parentheses

x^2-81x-2=0

a = 1; b = -81; c = -2;
Δ = b2-4ac
Δ = -812-4·1·(-2)
Δ = 6569
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-81)-\sqrt{6569}}{2*1}=\frac{81-\sqrt{6569}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-81)+\sqrt{6569}}{2*1}=\frac{81+\sqrt{6569}}{2}
$