X-1/5x=18

Solution for X-1/5x=18 equation:

X-1/5X=18

We move all terms to the left:

X-1/5X-(18)=0


Domain of the equation: 5X!=0

X!=0/5

X!=0

X∈R


We multiply all the terms by the denominator


X*5X-18*5X-1=0

Wy multiply elements

5X^2-90X-1=0

a = 5; b = -90; c = -1;
Δ = b2-4ac
Δ = -902-4·5·(-1)
Δ = 8120
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:

$\sqrt{\Delta}=\sqrt{8120}=\sqrt{4*2030}=\sqrt{4}*\sqrt{2030}=2\sqrt{2030}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-2\sqrt{2030}}{2*5}=\frac{90-2\sqrt{2030}}{10}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+2\sqrt{2030}}{2*5}=\frac{90+2\sqrt{2030}}{10}
$