X-1/5x=76

Solution for X-1/5x=76 equation:

X-1/5X=76

We move all terms to the left:

X-1/5X-(76)=0


Domain of the equation: 5X!=0

X!=0/5

X!=0

X∈R


We multiply all the terms by the denominator


X*5X-76*5X-1=0

Wy multiply elements

5X^2-380X-1=0

a = 5; b = -380; c = -1;
Δ = b2-4ac
Δ = -3802-4·5·(-1)
Δ = 144420
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:

$\sqrt{\Delta}=\sqrt{144420}=\sqrt{4*36105}=\sqrt{4}*\sqrt{36105}=2\sqrt{36105}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-380)-2\sqrt{36105}}{2*5}=\frac{380-2\sqrt{36105}}{10}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-380)+2\sqrt{36105}}{2*5}=\frac{380+2\sqrt{36105}}{10}
$