8r^2-16r=10

Solution for 8r^2-16r=10 equation:

8r^2-16r=10

We move all terms to the left:

8r^2-16r-(10)=0

a = 8; b = -16; c = -10;
Δ = b2-4ac
Δ = -162-4·8·(-10)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-24}{2*8}=\frac{-8}{16}
=-1/2
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+24}{2*8}=\frac{40}{16}
=2+1/2
$