-4r(r+6)=-57

Solution for -4r(r+6)=-57 equation:

-4r(r+6)=-57

We move all terms to the left:

-4r(r+6)-(-57)=0

We add all the numbers together, and all the variables

-4r(r+6)+57=0

We multiply parentheses

-4r^2-24r+57=0

a = -4; b = -24; c = +57;
Δ = b2-4ac
Δ = -242-4·(-4)·57
Δ = 1488
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:

$\sqrt{\Delta}=\sqrt{1488}=\sqrt{16*93}=\sqrt{16}*\sqrt{93}=4\sqrt{93}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{93}}{2*-4}=\frac{24-4\sqrt{93}}{-8}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{93}}{2*-4}=\frac{24+4\sqrt{93}}{-8}
$