1.5x^2-x-2.5=0

Solution for 1.5x^2-x-2.5=0 equation:

1.5x^2-x-2.5=0

We add all the numbers together, and all the variables

1.5x^2-1x-2.5=0

a = 1.5; b = -1; c = -2.5;
Δ = b2-4ac
Δ = -12-4·1.5·(-2.5)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-4}{2*1.5}=\frac{-3}{3}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+4}{2*1.5}=\frac{5}{3}
=1+2/3
$