8r^2+12r=21

Solution for 8r^2+12r=21 equation:

8r^2+12r=21

We move all terms to the left:

8r^2+12r-(21)=0

a = 8; b = 12; c = -21;
Δ = b2-4ac
Δ = 122-4·8·(-21)
Δ = 816
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:

$\sqrt{\Delta}=\sqrt{816}=\sqrt{16*51}=\sqrt{16}*\sqrt{51}=4\sqrt{51}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{51}}{2*8}=\frac{-12-4\sqrt{51}}{16}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{51}}{2*8}=\frac{-12+4\sqrt{51}}{16}
$