12x^2-41x-24=0

Solution for 12x^2-41x-24=0 equation:

12x^2-41x-24=0

a = 12; b = -41; c = -24;
Δ = b2-4ac
Δ = -412-4·12·(-24)
Δ = 2833
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-41)-\sqrt{2833}}{2*12}=\frac{41-\sqrt{2833}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-41)+\sqrt{2833}}{2*12}=\frac{41+\sqrt{2833}}{24}
$