1=0,09x^2-1,836x+9

Solution for 1=0,09x^2-1,836x+9 equation:

1=0.09x^2-1.836x+9

We move all terms to the left:

1-(0.09x^2-1.836x+9)=0

We get rid of parentheses

-0.09x^2+1.836x-9+1=0

We add all the numbers together, and all the variables

-0.09x^2+1.836x-8=0

a = -0.09; b = 1.836; c = -8;
Δ = b2-4ac
Δ = 1.8362-4·(-0.09)·(-8)
Δ = 0.490896
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{-(1.836)-\sqrt{0.490896}}{2*-0.09}=\frac{-1.836-\sqrt{0.490896}}{-0.18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1.836)+\sqrt{0.490896}}{2*-0.09}=\frac{-1.836+\sqrt{0.490896}}{-0.18}
$