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

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

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

We move all terms to the left:

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

We multiply parentheses

3x^2+12x-(2(x-1))=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+12x-2x+2=0

We add all the numbers together, and all the variables

3x^2+10x+2=0

a = 3; b = 10; c = +2;
Δ = b2-4ac
Δ = 102-4·3·2
Δ = 76
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{19}}{2*3}=\frac{-10-2\sqrt{19}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{19}}{2*3}=\frac{-10+2\sqrt{19}}{6}
$