3x-2x^2=0.15

Solution for 3x-2x^2=0.15 equation:

3x-2x^2=0.15

We move all terms to the left:

3x-2x^2-(0.15)=0

We add all the numbers together, and all the variables

-2x^2+3x-0.15=0

a = -2; b = 3; c = -0.15;
Δ = b2-4ac
Δ = 32-4·(-2)·(-0.15)
Δ = 7.8
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{-(3)-\sqrt{7.8}}{2*-2}=\frac{-3-\sqrt{7.8}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{7.8}}{2*-2}=\frac{-3+\sqrt{7.8}}{-4}
$