1/5x-16=4x

Solution for 1/5x-16=4x equation:

1/5x-16=4x

We move all terms to the left:

1/5x-16-(4x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-4x+1/5x-16=0

We multiply all the terms by the denominator


-4x*5x-16*5x+1=0

Wy multiply elements

-20x^2-80x+1=0

a = -20; b = -80; c = +1;
Δ = b2-4ac
Δ = -802-4·(-20)·1
Δ = 6480
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:

$\sqrt{\Delta}=\sqrt{6480}=\sqrt{1296*5}=\sqrt{1296}*\sqrt{5}=36\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-36\sqrt{5}}{2*-20}=\frac{80-36\sqrt{5}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+36\sqrt{5}}{2*-20}=\frac{80+36\sqrt{5}}{-40}
$