0.09+0.3x+x^2=1

Solution for 0.09+0.3x+x^2=1 equation:

0.09+0.3x+x^2=1

We move all terms to the left:

0.09+0.3x+x^2-(1)=0

We add all the numbers together, and all the variables

x^2+0.3x-0.91=0

a = 1; b = 0.3; c = -0.91;
Δ = b2-4ac
Δ = 0.32-4·1·(-0.91)
Δ = 3.73
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{-(0.3)-\sqrt{3.73}}{2*1}=\frac{-0.3-\sqrt{3.73}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.3)+\sqrt{3.73}}{2*1}=\frac{-0.3+\sqrt{3.73}}{2}
$