0.13x+1=0.09x2

Solution for 0.13x+1=0.09x2 equation:

0.13x+1=0.09x^2

We move all terms to the left:

0.13x+1-(0.09x^2)=0

We get rid of parentheses

-0.09x^2+0.13x+1=0

a = -0.09; b = 0.13; c = +1;
Δ = b2-4ac
Δ = 0.132-4·(-0.09)·1
Δ = 0.3769
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{-(0.13)-\sqrt{0.3769}}{2*-0.09}=\frac{-0.13-\sqrt{0.3769}}{-0.18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.13)+\sqrt{0.3769}}{2*-0.09}=\frac{-0.13+\sqrt{0.3769}}{-0.18}
$