24r^2+14r-90=0

Solution for 24r^2+14r-90=0 equation:

24r^2+14r-90=0

a = 24; b = 14; c = -90;
Δ = b2-4ac
Δ = 142-4·24·(-90)
Δ = 8836
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8836}=94$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-94}{2*24}=\frac{-108}{48}
=-2+1/4
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+94}{2*24}=\frac{80}{48}
=1+2/3
$