1.5x^2-6x-40=0

Solution for 1.5x^2-6x-40=0 equation:

1.5x^2-6x-40=0

a = 1.5; b = -6; c = -40;
Δ = b2-4ac
Δ = -62-4·1.5·(-40)
Δ = 276
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:

$\sqrt{\Delta}=\sqrt{276}=\sqrt{4*69}=\sqrt{4}*\sqrt{69}=2\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{69}}{2*1.5}=\frac{6-2\sqrt{69}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{69}}{2*1.5}=\frac{6+2\sqrt{69}}{3}
$