x=-0.1x^2+1.5x+0.4

Solution for x=-0.1x^2+1.5x+0.4 equation:

x=-0.1x^2+1.5x+0.4

We move all terms to the left:

x-(-0.1x^2+1.5x+0.4)=0

We get rid of parentheses

0.1x^2-1.5x+x-0.4=0

We add all the numbers together, and all the variables

0.1x^2-0.5x-0.4=0

a = 0.1; b = -0.5; c = -0.4;
Δ = b2-4ac
Δ = -0.52-4·0.1·(-0.4)
Δ = 0.41
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{0.41}}{2*0.1}=\frac{0.5-\sqrt{0.41}}{0.2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.5)+\sqrt{0.41}}{2*0.1}=\frac{0.5+\sqrt{0.41}}{0.2}
$