24x2-65x+21=0

Solution for 24x2-65x+21=0 equation:

24x^2-65x+21=0

a = 24; b = -65; c = +21;
Δ = b2-4ac
Δ = -652-4·24·21
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-65)-47}{2*24}=\frac{18}{48}
=3/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-65)+47}{2*24}=\frac{112}{48}
=2+1/3
$