24x^2-89x+76=0

Solution for 24x^2-89x+76=0 equation:

24x^2-89x+76=0

a = 24; b = -89; c = +76;
Δ = b2-4ac
Δ = -892-4·24·76
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-89)-25}{2*24}=\frac{64}{48}
=1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-89)+25}{2*24}=\frac{114}{48}
=2+3/8
$