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

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

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

We move all terms to the left:

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

We multiply parentheses

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


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

4(x+2)

We multiply parentheses

4x+8

Back to the equation:

-(4x+8)


We get rid of parentheses

3x^2-3x-4x-8=0

We add all the numbers together, and all the variables

3x^2-7x-8=0

a = 3; b = -7; c = -8;
Δ = b2-4ac
Δ = -72-4·3·(-8)
Δ = 145
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{-(-7)-\sqrt{145}}{2*3}=\frac{7-\sqrt{145}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{145}}{2*3}=\frac{7+\sqrt{145}}{6}
$