24x^2+22x-65=0

Solution for 24x^2+22x-65=0 equation:

24x^2+22x-65=0

a = 24; b = 22; c = -65;
Δ = b2-4ac
Δ = 222-4·24·(-65)
Δ = 6724
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6724}=82$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-82}{2*24}=\frac{-104}{48}
=-2+1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+82}{2*24}=\frac{60}{48}
=1+1/4
$