5x^2+24x-240=0

Solution for 5x^2+24x-240=0 equation:

5x^2+24x-240=0

a = 5; b = 24; c = -240;
Δ = b2-4ac
Δ = 242-4·5·(-240)
Δ = 5376
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:

$\sqrt{\Delta}=\sqrt{5376}=\sqrt{256*21}=\sqrt{256}*\sqrt{21}=16\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-16\sqrt{21}}{2*5}=\frac{-24-16\sqrt{21}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+16\sqrt{21}}{2*5}=\frac{-24+16\sqrt{21}}{10}
$