-4r(r+5)=-59

Solution for -4r(r+5)=-59 equation:

-4r(r+5)=-59

We move all terms to the left:

-4r(r+5)-(-59)=0

We add all the numbers together, and all the variables

-4r(r+5)+59=0

We multiply parentheses

-4r^2-20r+59=0

a = -4; b = -20; c = +59;
Δ = b2-4ac
Δ = -202-4·(-4)·59
Δ = 1344
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:

$\sqrt{\Delta}=\sqrt{1344}=\sqrt{64*21}=\sqrt{64}*\sqrt{21}=8\sqrt{21}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-8\sqrt{21}}{2*-4}=\frac{20-8\sqrt{21}}{-8}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+8\sqrt{21}}{2*-4}=\frac{20+8\sqrt{21}}{-8}
$