X+1/5x=72

Solution for X+1/5x=72 equation:

X+1/5X=72

We move all terms to the left:

X+1/5X-(72)=0


Domain of the equation: 5X!=0

X!=0/5

X!=0

X∈R


We multiply all the terms by the denominator


X*5X-72*5X+1=0

Wy multiply elements

5X^2-360X+1=0

a = 5; b = -360; c = +1;
Δ = b2-4ac
Δ = -3602-4·5·1
Δ = 129580
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:

$\sqrt{\Delta}=\sqrt{129580}=\sqrt{4*32395}=\sqrt{4}*\sqrt{32395}=2\sqrt{32395}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-360)-2\sqrt{32395}}{2*5}=\frac{360-2\sqrt{32395}}{10}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-360)+2\sqrt{32395}}{2*5}=\frac{360+2\sqrt{32395}}{10}
$