x^2=-1.5x

Solution for x^2=-1.5x equation:

x^2=-1.5x

We move all terms to the left:

x^2-(-1.5x)=0

We get rid of parentheses

x^2+1.5x=0

a = 1; b = 1.5; c = 0;
Δ = b2-4ac
Δ = 1.52-4·1·0
Δ = 2.25
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{-(1.5)-\sqrt{2.25}}{2*1}=\frac{-1.5-\sqrt{2.25}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1.5)+\sqrt{2.25}}{2*1}=\frac{-1.5+\sqrt{2.25}}{2}
$