24x^2+116x+120=0

Solution for 24x^2+116x+120=0 equation:

24x^2+116x+120=0

a = 24; b = 116; c = +120;
Δ = b2-4ac
Δ = 1162-4·24·120
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(116)-44}{2*24}=\frac{-160}{48}
=-3+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(116)+44}{2*24}=\frac{-72}{48}
=-1+1/2
$