X-1/5x=16

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

X-1/5X=16

We move all terms to the left:

X-1/5X-(16)=0


Domain of the equation: 5X!=0

X!=0/5

X!=0

X∈R


We multiply all the terms by the denominator


X*5X-16*5X-1=0

Wy multiply elements

5X^2-80X-1=0

a = 5; b = -80; c = -1;
Δ = b2-4ac
Δ = -802-4·5·(-1)
Δ = 6420
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:

$\sqrt{\Delta}=\sqrt{6420}=\sqrt{4*1605}=\sqrt{4}*\sqrt{1605}=2\sqrt{1605}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-2\sqrt{1605}}{2*5}=\frac{80-2\sqrt{1605}}{10}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+2\sqrt{1605}}{2*5}=\frac{80+2\sqrt{1605}}{10}
$