-1.5*x^2=-0.5x-1.3

Solution for -1.5*x^2=-0.5x-1.3 equation:

-1.5x^2=-0.5x-1.3

We move all terms to the left:

-1.5x^2-(-0.5x-1.3)=0

We get rid of parentheses

-1.5x^2+0.5x+1.3=0

a = -1.5; b = 0.5; c = +1.3;
Δ = b2-4ac
Δ = 0.52-4·(-1.5)·1.3
Δ = 8.05
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{-(0.5)-\sqrt{8.05}}{2*-1.5}=\frac{-0.5-\sqrt{8.05}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.5)+\sqrt{8.05}}{2*-1.5}=\frac{-0.5+\sqrt{8.05}}{-3}
$