24x^2-200x-400=0

Solution for 24x^2-200x-400=0 equation:

24x^2-200x-400=0

a = 24; b = -200; c = -400;
Δ = b2-4ac
Δ = -2002-4·24·(-400)
Δ = 78400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{78400}=280$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-280}{2*24}=\frac{-80}{48}
=-1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+280}{2*24}=\frac{480}{48}
=10
$