24x2+42x-216=0

Solution for 24x2+42x-216=0 equation:

24x^2+42x-216=0

a = 24; b = 42; c = -216;
Δ = b2-4ac
Δ = 422-4·24·(-216)
Δ = 22500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{22500}=150$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-150}{2*24}=\frac{-192}{48}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+150}{2*24}=\frac{108}{48}
=2+1/4
$