3.2x(x-1)=2.2x+1

Solution for 3.2x(x-1)=2.2x+1 equation:

3.2x(x-1)=2.2x+1

We move all terms to the left:

3.2x(x-1)-(2.2x+1)=0

We multiply parentheses

3x^2-3x-(2.2x+1)=0

We get rid of parentheses

3x^2-3x-2.2x-1=0

We add all the numbers together, and all the variables

3x^2-5.2x-1=0

a = 3; b = -5.2; c = -1;
Δ = b2-4ac
Δ = -5.22-4·3·(-1)
Δ = 39.04
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{-(-5.2)-\sqrt{39.04}}{2*3}=\frac{5.2-\sqrt{39.04}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5.2)+\sqrt{39.04}}{2*3}=\frac{5.2+\sqrt{39.04}}{6}
$