-20.8x^2+3.7x+2.9=x

Solution for -20.8x^2+3.7x+2.9=x equation:

-20.8x^2+3.7x+2.9=x

We move all terms to the left:

-20.8x^2+3.7x+2.9-(x)=0

We add all the numbers together, and all the variables

-20.8x^2+2.7x+2.9=0

a = -20.8; b = 2.7; c = +2.9;
Δ = b2-4ac
Δ = 2.72-4·(-20.8)·2.9
Δ = 248.57
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{-(2.7)-\sqrt{248.57}}{2*-20.8}=\frac{-2.7-\sqrt{248.57}}{-41.6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2.7)+\sqrt{248.57}}{2*-20.8}=\frac{-2.7+\sqrt{248.57}}{-41.6}
$