-5-3(4-r)r=9

Solution for -5-3(4-r)r=9 equation:

-5-3(4-r)r=9

We move all terms to the left:

-5-3(4-r)r-(9)=0

We add all the numbers together, and all the variables

-3(-1r+4)r-5-9=0

We add all the numbers together, and all the variables

-3(-1r+4)r-14=0

We multiply parentheses

3r^2-12r-14=0

a = 3; b = -12; c = -14;
Δ = b2-4ac
Δ = -122-4·3·(-14)
Δ = 312
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:

$\sqrt{\Delta}=\sqrt{312}=\sqrt{4*78}=\sqrt{4}*\sqrt{78}=2\sqrt{78}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{78}}{2*3}=\frac{12-2\sqrt{78}}{6}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{78}}{2*3}=\frac{12+2\sqrt{78}}{6}
$