2=1+9x-5x^2

Solution for 2=1+9x-5x^2 equation:

2=1+9x-5x^2

We move all terms to the left:

2-(1+9x-5x^2)=0

We get rid of parentheses

5x^2-9x-1+2=0

We add all the numbers together, and all the variables

5x^2-9x+1=0

a = 5; b = -9; c = +1;
Δ = b2-4ac
Δ = -92-4·5·1
Δ = 61
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{-(-9)-\sqrt{61}}{2*5}=\frac{9-\sqrt{61}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{61}}{2*5}=\frac{9+\sqrt{61}}{10}
$