(3x-2)(x-4)=5x(x-1)

Solution for (3x-2)(x-4)=5x(x-1) equation:

(3x-2)(x-4)=5x(x-1)

We move all terms to the left:

(3x-2)(x-4)-(5x(x-1))=0

We multiply parentheses ..

(+3x^2-12x-2x+8)-(5x(x-1))=0


We calculate terms in parentheses: -(5x(x-1)), so:

5x(x-1)

We multiply parentheses

5x^2-5x

Back to the equation:

-(5x^2-5x)


We get rid of parentheses

3x^2-5x^2-12x-2x+5x+8=0

We add all the numbers together, and all the variables

-2x^2-9x+8=0

a = -2; b = -9; c = +8;
Δ = b2-4ac
Δ = -92-4·(-2)·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{-(-9)-\sqrt{145}}{2*-2}=\frac{9-\sqrt{145}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{145}}{2*-2}=\frac{9+\sqrt{145}}{-4}
$