3x+0.05=x(x+0.10)

Solution for 3x+0.05=x(x+0.10) equation:

3x+0.05=x(x+0.10)

We move all terms to the left:

3x+0.05-(x(x+0.10))=0

We add all the numbers together, and all the variables

3x-(x(x+0.1))+0.05=0


We calculate terms in parentheses: -(x(x+0.1)), so:

x(x+0.1)

We multiply parentheses

x^2+0.1x

Back to the equation:

-(x^2+0.1x)


We get rid of parentheses

-x^2+3x-0.1x+0.05=0

We add all the numbers together, and all the variables

-1x^2+2.9x+0.05=0

a = -1; b = 2.9; c = +0.05;
Δ = b2-4ac
Δ = 2.92-4·(-1)·0.05
Δ = 8.61
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{-(2.9)-\sqrt{8.61}}{2*-1}=\frac{-2.9-\sqrt{8.61}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2.9)+\sqrt{8.61}}{2*-1}=\frac{-2.9+\sqrt{8.61}}{-2}
$