r(5+2r)-5(r-4)=52

Solution for r(5+2r)-5(r-4)=52 equation:

r(5+2r)-5(r-4)=52

We move all terms to the left:

r(5+2r)-5(r-4)-(52)=0

We add all the numbers together, and all the variables

r(2r+5)-5(r-4)-52=0

We multiply parentheses

2r^2+5r-5r+20-52=0

We add all the numbers together, and all the variables

2r^2-32=0

a = 2; b = 0; c = -32;
Δ = b2-4ac
Δ = 02-4·2·(-32)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16}{2*2}=\frac{-16}{4}
=-4
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16}{2*2}=\frac{16}{4}
=4
$