24x-32+5x^2=0

Solution for 24x-32+5x^2=0 equation:

24x-32+5x^2=0

a = 5; b = 24; c = -32;
Δ = b2-4ac
Δ = 242-4·5·(-32)
Δ = 1216
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:

$\sqrt{\Delta}=\sqrt{1216}=\sqrt{64*19}=\sqrt{64}*\sqrt{19}=8\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-8\sqrt{19}}{2*5}=\frac{-24-8\sqrt{19}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+8\sqrt{19}}{2*5}=\frac{-24+8\sqrt{19}}{10}
$