X+1/5x=240

Solution for X+1/5x=240 equation:

X+1/5X=240

We move all terms to the left:

X+1/5X-(240)=0


Domain of the equation: 5X!=0

X!=0/5

X!=0

X∈R


We multiply all the terms by the denominator


X*5X-240*5X+1=0

Wy multiply elements

5X^2-1200X+1=0

a = 5; b = -1200; c = +1;
Δ = b2-4ac
Δ = -12002-4·5·1
Δ = 1439980
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:

$\sqrt{\Delta}=\sqrt{1439980}=\sqrt{4*359995}=\sqrt{4}*\sqrt{359995}=2\sqrt{359995}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1200)-2\sqrt{359995}}{2*5}=\frac{1200-2\sqrt{359995}}{10}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1200)+2\sqrt{359995}}{2*5}=\frac{1200+2\sqrt{359995}}{10}
$