7r(2r+8)=32

Solution for 7r(2r+8)=32 equation:

7r(2r+8)=32

We move all terms to the left:

7r(2r+8)-(32)=0

We multiply parentheses

14r^2+56r-32=0

a = 14; b = 56; c = -32;
Δ = b2-4ac
Δ = 562-4·14·(-32)
Δ = 4928
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:

$\sqrt{\Delta}=\sqrt{4928}=\sqrt{64*77}=\sqrt{64}*\sqrt{77}=8\sqrt{77}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-8\sqrt{77}}{2*14}=\frac{-56-8\sqrt{77}}{28}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+8\sqrt{77}}{2*14}=\frac{-56+8\sqrt{77}}{28}
$