X-1/5x=55

Solution for X-1/5x=55 equation:

X-1/5X=55

We move all terms to the left:

X-1/5X-(55)=0


Domain of the equation: 5X!=0

X!=0/5

X!=0

X∈R


We multiply all the terms by the denominator


X*5X-55*5X-1=0

Wy multiply elements

5X^2-275X-1=0

a = 5; b = -275; c = -1;
Δ = b2-4ac
Δ = -2752-4·5·(-1)
Δ = 75645
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:

$\sqrt{\Delta}=\sqrt{75645}=\sqrt{15129*5}=\sqrt{15129}*\sqrt{5}=123\sqrt{5}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-275)-123\sqrt{5}}{2*5}=\frac{275-123\sqrt{5}}{10}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-275)+123\sqrt{5}}{2*5}=\frac{275+123\sqrt{5}}{10}
$