0=1.5x^2-0.75x-1.

Solution for 0=1.5x^2-0.75x-1. equation:

0=1.5x^2-0.75x-1.

We move all terms to the left:

0-(1.5x^2-0.75x-1.)=0

We add all the numbers together, and all the variables

-(1.5x^2-0.75x-1.)=0

We get rid of parentheses

-1.5x^2+0.75x+1.=0

We add all the numbers together, and all the variables

-1.5x^2+0.75x+1=0

a = -1.5; b = 0.75; c = +1;
Δ = b2-4ac
Δ = 0.752-4·(-1.5)·1
Δ = 6.5625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0.75)-\sqrt{6.5625}}{2*-1.5}=\frac{-0.75-\sqrt{6.5625}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.75)+\sqrt{6.5625}}{2*-1.5}=\frac{-0.75+\sqrt{6.5625}}{-3}
$