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

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

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

We move all terms to the left:

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

We multiply parentheses

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


We calculate terms in parentheses: -(4x(x-1)), so:

4x(x-1)

We multiply parentheses

4x^2-4x

Back to the equation:

-(4x^2-4x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

-4x^2+7x+3=0

a = -4; b = 7; c = +3;
Δ = b2-4ac
Δ = 72-4·(-4)·3
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{-(7)-\sqrt{97}}{2*-4}=\frac{-7-\sqrt{97}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{97}}{2*-4}=\frac{-7+\sqrt{97}}{-8}
$