3x(x-1)-4=2(x+1)

Solution for 3x(x-1)-4=2(x+1) equation:

3x(x-1)-4=2(x+1)

We move all terms to the left:

3x(x-1)-4-(2(x+1))=0

We multiply parentheses

3x^2-3x-(2(x+1))-4=0


We calculate terms in parentheses: -(2(x+1)), so:

2(x+1)

We multiply parentheses

2x+2

Back to the equation:

-(2x+2)


We get rid of parentheses

3x^2-3x-2x-2-4=0

We add all the numbers together, and all the variables

3x^2-5x-6=0

a = 3; b = -5; c = -6;
Δ = b2-4ac
Δ = -52-4·3·(-6)
Δ = 97
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)-\sqrt{97}}{2*3}=\frac{5-\sqrt{97}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{97}}{2*3}=\frac{5+\sqrt{97}}{6}
$