-4r(r+2)=-62

Solution for -4r(r+2)=-62 equation:

-4r(r+2)=-62

We move all terms to the left:

-4r(r+2)-(-62)=0

We add all the numbers together, and all the variables

-4r(r+2)+62=0

We multiply parentheses

-4r^2-8r+62=0

a = -4; b = -8; c = +62;
Δ = b2-4ac
Δ = -82-4·(-4)·62
Δ = 1056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1056}=\sqrt{16*66}=\sqrt{16}*\sqrt{66}=4\sqrt{66}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{66}}{2*-4}=\frac{8-4\sqrt{66}}{-8}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{66}}{2*-4}=\frac{8+4\sqrt{66}}{-8}
$