x^2-7x-(1/7)=0

Solution for x^2-7x-(1/7)=0 equation:

x^2-7x-(1/7)=0

We add all the numbers together, and all the variables

x^2-7x-(+1/7)=0

We get rid of parentheses

x^2-7x-1/7=0

We multiply all the terms by the denominator


x^2*7-7x*7-1=0

Wy multiply elements

7x^2-49x-1=0

a = 7; b = -49; c = -1;
Δ = b2-4ac
Δ = -492-4·7·(-1)
Δ = 2429
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-49)-\sqrt{2429}}{2*7}=\frac{49-\sqrt{2429}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-49)+\sqrt{2429}}{2*7}=\frac{49+\sqrt{2429}}{14}
$