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

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

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

We move all terms to the left:

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

We multiply parentheses

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


We calculate terms in parentheses: -(2(x+4)), so:

2(x+4)

We multiply parentheses

2x+8

Back to the equation:

-(2x+8)


We get rid of parentheses

3x^2-3x-2x-8=0

We add all the numbers together, and all the variables

3x^2-5x-8=0

a = 3; b = -5; c = -8;
Δ = b2-4ac
Δ = -52-4·3·(-8)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-11}{2*3}=\frac{-6}{6}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+11}{2*3}=\frac{16}{6}
=2+2/3
$