-4r(r+6)=-62

Solution for -4r(r+6)=-62 equation:

-4r(r+6)=-62

We move all terms to the left:

-4r(r+6)-(-62)=0

We add all the numbers together, and all the variables

-4r(r+6)+62=0

We multiply parentheses

-4r^2-24r+62=0

a = -4; b = -24; c = +62;
Δ = b2-4ac
Δ = -242-4·(-4)·62
Δ = 1568
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:

$\sqrt{\Delta}=\sqrt{1568}=\sqrt{784*2}=\sqrt{784}*\sqrt{2}=28\sqrt{2}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-28\sqrt{2}}{2*-4}=\frac{24-28\sqrt{2}}{-8}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+28\sqrt{2}}{2*-4}=\frac{24+28\sqrt{2}}{-8}
$