15r^2-16r=16

Solution for 15r^2-16r=16 equation:

15r^2-16r=16

We move all terms to the left:

15r^2-16r-(16)=0

a = 15; b = -16; c = -16;
Δ = b2-4ac
Δ = -162-4·15·(-16)
Δ = 1216
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:

$\sqrt{\Delta}=\sqrt{1216}=\sqrt{64*19}=\sqrt{64}*\sqrt{19}=8\sqrt{19}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-8\sqrt{19}}{2*15}=\frac{16-8\sqrt{19}}{30}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+8\sqrt{19}}{2*15}=\frac{16+8\sqrt{19}}{30}
$