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

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

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

We move all terms to the left:

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

We multiply parentheses

5x-12x-(4x(2x-1))+6=0


We calculate terms in parentheses: -(4x(2x-1)), so:

4x(2x-1)

We multiply parentheses

8x^2-4x

Back to the equation:

-(8x^2-4x)


We add all the numbers together, and all the variables

-7x-(8x^2-4x)+6=0

We get rid of parentheses

-8x^2-7x+4x+6=0

We add all the numbers together, and all the variables

-8x^2-3x+6=0

a = -8; b = -3; c = +6;
Δ = b2-4ac
Δ = -32-4·(-8)·6
Δ = 201
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{-(-3)-\sqrt{201}}{2*-8}=\frac{3-\sqrt{201}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{201}}{2*-8}=\frac{3+\sqrt{201}}{-16}
$