x(18.91+x)=0.3

Solution for x(18.91+x)=0.3 equation:

x(18.91+x)=0.3

We move all terms to the left:

x(18.91+x)-(0.3)=0

We add all the numbers together, and all the variables

x(x+18.91)-(0.3)=0

We add all the numbers together, and all the variables

x(x+18.91)-0.3=0

We multiply parentheses

x^2+18.91x-0.3=0

a = 1; b = 18.91; c = -0.3;
Δ = b2-4ac
Δ = 18.912-4·1·(-0.3)
Δ = 358.7881
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{-(18.91)-\sqrt{358.7881}}{2*1}=\frac{-18.91-\sqrt{358.7881}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18.91)+\sqrt{358.7881}}{2*1}=\frac{-18.91+\sqrt{358.7881}}{2}
$