3x-4=4x(x-4)

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

3x-4=4x(x-4)

We move all terms to the left:

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


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

4x(x-4)

We multiply parentheses

4x^2-16x

Back to the equation:

-(4x^2-16x)


We get rid of parentheses

-4x^2+3x+16x-4=0

We add all the numbers together, and all the variables

-4x^2+19x-4=0

a = -4; b = 19; c = -4;
Δ = b2-4ac
Δ = 192-4·(-4)·(-4)
Δ = 297
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{297}=\sqrt{9*33}=\sqrt{9}*\sqrt{33}=3\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-3\sqrt{33}}{2*-4}=\frac{-19-3\sqrt{33}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+3\sqrt{33}}{2*-4}=\frac{-19+3\sqrt{33}}{-8}
$