1.5x-x^2=0.15

Solution for 1.5x-x^2=0.15 equation:

1.5x-x^2=0.15

We move all terms to the left:

1.5x-x^2-(0.15)=0

We add all the numbers together, and all the variables

-1x^2+1.5x-0.15=0

a = -1; b = 1.5; c = -0.15;
Δ = b2-4ac
Δ = 1.52-4·(-1)·(-0.15)
Δ = 1.65
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{1.65}}{2*-1}=\frac{-1.5-\sqrt{1.65}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1.5)+\sqrt{1.65}}{2*-1}=\frac{-1.5+\sqrt{1.65}}{-2}
$