7x^2+17x-1=-7

Solution for 7x^2+17x-1=-7 equation:

7x^2+17x-1=-7

We move all terms to the left:

7x^2+17x-1-(-7)=0

We add all the numbers together, and all the variables

7x^2+17x+6=0

a = 7; b = 17; c = +6;
Δ = b2-4ac
Δ = 172-4·7·6
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-11}{2*7}=\frac{-28}{14}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+11}{2*7}=\frac{-6}{14}
=-3/7
$