5r-(2r+8)5r=16

Solution for 5r-(2r+8)5r=16 equation:

5r-(2r+8)5r=16

We move all terms to the left:

5r-(2r+8)5r-(16)=0

We multiply parentheses

-10r^2+5r-40r-16=0

We add all the numbers together, and all the variables

-10r^2-35r-16=0

a = -10; b = -35; c = -16;
Δ = b2-4ac
Δ = -352-4·(-10)·(-16)
Δ = 585
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:

$\sqrt{\Delta}=\sqrt{585}=\sqrt{9*65}=\sqrt{9}*\sqrt{65}=3\sqrt{65}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-3\sqrt{65}}{2*-10}=\frac{35-3\sqrt{65}}{-20}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+3\sqrt{65}}{2*-10}=\frac{35+3\sqrt{65}}{-20}
$