7r^2-17r-17=-5

Solution for 7r^2-17r-17=-5 equation:

7r^2-17r-17=-5

We move all terms to the left:

7r^2-17r-17-(-5)=0

We add all the numbers together, and all the variables

7r^2-17r-12=0

a = 7; b = -17; c = -12;
Δ = b2-4ac
Δ = -172-4·7·(-12)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-25}{2*7}=\frac{-8}{14}
=-4/7
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+25}{2*7}=\frac{42}{14}
=3
$