8r+2r(r+6)=37

Solution for 8r+2r(r+6)=37 equation:

8r+2r(r+6)=37

We move all terms to the left:

8r+2r(r+6)-(37)=0

We multiply parentheses

2r^2+8r+12r-37=0

We add all the numbers together, and all the variables

2r^2+20r-37=0

a = 2; b = 20; c = -37;
Δ = b2-4ac
Δ = 202-4·2·(-37)
Δ = 696
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:

$\sqrt{\Delta}=\sqrt{696}=\sqrt{4*174}=\sqrt{4}*\sqrt{174}=2\sqrt{174}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{174}}{2*2}=\frac{-20-2\sqrt{174}}{4}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{174}}{2*2}=\frac{-20+2\sqrt{174}}{4}
$