6r^2+66r+171=3

Solution for 6r^2+66r+171=3 equation:

6r^2+66r+171=3

We move all terms to the left:

6r^2+66r+171-(3)=0

We add all the numbers together, and all the variables

6r^2+66r+168=0

a = 6; b = 66; c = +168;
Δ = b2-4ac
Δ = 662-4·6·168
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(66)-18}{2*6}=\frac{-84}{12}
=-7
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(66)+18}{2*6}=\frac{-48}{12}
=-4
$