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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

3x^2-1x-4=0

a = 3; b = -1; c = -4;
Δ = b2-4ac
Δ = -12-4·3·(-4)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-7}{2*3}=\frac{-6}{6}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+7}{2*3}=\frac{8}{6}
=1+1/3
$