7r^2-3r-11=-5

Solution for 7r^2-3r-11=-5 equation:

7r^2-3r-11=-5

We move all terms to the left:

7r^2-3r-11-(-5)=0

We add all the numbers together, and all the variables

7r^2-3r-6=0

a = 7; b = -3; c = -6;
Δ = b2-4ac
Δ = -32-4·7·(-6)
Δ = 177
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{177}}{2*7}=\frac{3-\sqrt{177}}{14}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{177}}{2*7}=\frac{3+\sqrt{177}}{14}
$