X^2-17x=1/5

Solution for X^2-17x=1/5 equation:

X^2-17X=1/5

We move all terms to the left:

X^2-17X-(1/5)=0

We add all the numbers together, and all the variables

X^2-17X-(+1/5)=0

We get rid of parentheses

X^2-17X-1/5=0

We multiply all the terms by the denominator


X^2*5-17X*5-1=0

Wy multiply elements

5X^2-85X-1=0

a = 5; b = -85; c = -1;
Δ = b2-4ac
Δ = -852-4·5·(-1)
Δ = 7245
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:

$\sqrt{\Delta}=\sqrt{7245}=\sqrt{9*805}=\sqrt{9}*\sqrt{805}=3\sqrt{805}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-85)-3\sqrt{805}}{2*5}=\frac{85-3\sqrt{805}}{10}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-85)+3\sqrt{805}}{2*5}=\frac{85+3\sqrt{805}}{10}
$