22=(3x+2)(x-1)

Solution for 22=(3x+2)(x-1) equation:

22=(3x+2)(x-1)

We move all terms to the left:

22-((3x+2)(x-1))=0

We multiply parentheses ..

-((+3x^2-3x+2x-2))+22=0


We calculate terms in parentheses: -((+3x^2-3x+2x-2)), so:

(+3x^2-3x+2x-2)

We get rid of parentheses

3x^2-3x+2x-2

We add all the numbers together, and all the variables

3x^2-1x-2

Back to the equation:

-(3x^2-1x-2)


We get rid of parentheses

-3x^2+1x+2+22=0

We add all the numbers together, and all the variables

-3x^2+x+24=0

a = -3; b = 1; c = +24;
Δ = b2-4ac
Δ = 12-4·(-3)·24
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-17}{2*-3}=\frac{-18}{-6}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+17}{2*-3}=\frac{16}{-6}
=-2+2/3
$