x=-0.9x^2+2.8x+2.4

Solution for x=-0.9x^2+2.8x+2.4 equation:

x=-0.9x^2+2.8x+2.4

We move all terms to the left:

x-(-0.9x^2+2.8x+2.4)=0

We get rid of parentheses

0.9x^2-2.8x+x-2.4=0

We add all the numbers together, and all the variables

0.9x^2-1.8x-2.4=0

a = 0.9; b = -1.8; c = -2.4;
Δ = b2-4ac
Δ = -1.82-4·0.9·(-2.4)
Δ = 11.88
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{-(-1.8)-\sqrt{11.88}}{2*0.9}=\frac{1.8-\sqrt{11.88}}{1.8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1.8)+\sqrt{11.88}}{2*0.9}=\frac{1.8+\sqrt{11.88}}{1.8}
$