21x^2-65x+24=0

Solution for 21x^2-65x+24=0 equation:

21x^2-65x+24=0

a = 21; b = -65; c = +24;
Δ = b2-4ac
Δ = -652-4·21·24
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*21}=\frac{18}{42}
=3/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-65)+47}{2*21}=\frac{112}{42}
=2+2/3
$