80+24x-1.5x^2=0

Solution for 80+24x-1.5x^2=0 equation:

80+24x-1.5x^2=0

a = -1.5; b = 24; c = +80;
Δ = b2-4ac
Δ = 242-4·(-1.5)·80
Δ = 1056
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:

$\sqrt{\Delta}=\sqrt{1056}=\sqrt{16*66}=\sqrt{16}*\sqrt{66}=4\sqrt{66}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{66}}{2*-1.5}=\frac{-24-4\sqrt{66}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{66}}{2*-1.5}=\frac{-24+4\sqrt{66}}{-3}
$