16r^2-180r-144=0

Solution for 16r^2-180r-144=0 equation:

16r^2-180r-144=0

a = 16; b = -180; c = -144;
Δ = b2-4ac
Δ = -1802-4·16·(-144)
Δ = 41616
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{41616}=204$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-204}{2*16}=\frac{-24}{32}
=-3/4
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+204}{2*16}=\frac{384}{32}
=12
$