10x^2+24x=19584

Solution for 10x^2+24x=19584 equation:

10x^2+24x=19584

We move all terms to the left:

10x^2+24x-(19584)=0

a = 10; b = 24; c = -19584;
Δ = b2-4ac
Δ = 242-4·10·(-19584)
Δ = 783936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{783936}=\sqrt{576*1361}=\sqrt{576}*\sqrt{1361}=24\sqrt{1361}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-24\sqrt{1361}}{2*10}=\frac{-24-24\sqrt{1361}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24\sqrt{1361}}{2*10}=\frac{-24+24\sqrt{1361}}{20}
$