8r^2+24r=-17

Solution for 8r^2+24r=-17 equation:

8r^2+24r=-17

We move all terms to the left:

8r^2+24r-(-17)=0

We add all the numbers together, and all the variables

8r^2+24r+17=0

a = 8; b = 24; c = +17;
Δ = b2-4ac
Δ = 242-4·8·17
Δ = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{2}}{2*8}=\frac{-24-4\sqrt{2}}{16}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{2}}{2*8}=\frac{-24+4\sqrt{2}}{16}
$