-4r(r+5)=-71

Solution for -4r(r+5)=-71 equation:

-4r(r+5)=-71

We move all terms to the left:

-4r(r+5)-(-71)=0

We add all the numbers together, and all the variables

-4r(r+5)+71=0

We multiply parentheses

-4r^2-20r+71=0

a = -4; b = -20; c = +71;
Δ = b2-4ac
Δ = -202-4·(-4)·71
Δ = 1536
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:

$\sqrt{\Delta}=\sqrt{1536}=\sqrt{256*6}=\sqrt{256}*\sqrt{6}=16\sqrt{6}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-16\sqrt{6}}{2*-4}=\frac{20-16\sqrt{6}}{-8}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+16\sqrt{6}}{2*-4}=\frac{20+16\sqrt{6}}{-8}
$