x(0.03+x)=0.91

Solution for x(0.03+x)=0.91 equation:

x(0.03+x)=0.91

We move all terms to the left:

x(0.03+x)-(0.91)=0

We add all the numbers together, and all the variables

x(x+0.03)-(0.91)=0

We add all the numbers together, and all the variables

x(x+0.03)-0.91=0

We multiply parentheses

x^2+0.03x-0.91=0

a = 1; b = 0.03; c = -0.91;
Δ = b2-4ac
Δ = 0.032-4·1·(-0.91)
Δ = 3.6409
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{-(0.03)-\sqrt{3.6409}}{2*1}=\frac{-0.03-\sqrt{3.6409}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.03)+\sqrt{3.6409}}{2*1}=\frac{-0.03+\sqrt{3.6409}}{2}
$