7x(x-5)=-1

Solution for 7x(x-5)=-1 equation:

7x(x-5)=-1

We move all terms to the left:

7x(x-5)-(-1)=0

We add all the numbers together, and all the variables

7x(x-5)+1=0

We multiply parentheses

7x^2-35x+1=0

a = 7; b = -35; c = +1;
Δ = b2-4ac
Δ = -352-4·7·1
Δ = 1197
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:

$\sqrt{\Delta}=\sqrt{1197}=\sqrt{9*133}=\sqrt{9}*\sqrt{133}=3\sqrt{133}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-3\sqrt{133}}{2*7}=\frac{35-3\sqrt{133}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+3\sqrt{133}}{2*7}=\frac{35+3\sqrt{133}}{14}
$