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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

-4x^2-1x+(3x+4)/3+16x=0

We multiply all the terms by the denominator


-4x^2*3-1x*3+(3x+4)+16x*3=0

Wy multiply elements

-12x^2-3x+(3x+4)+48x=0

We get rid of parentheses

-12x^2-3x+3x+48x+4=0

We add all the numbers together, and all the variables

-12x^2+48x+4=0

a = -12; b = 48; c = +4;
Δ = b2-4ac
Δ = 482-4·(-12)·4
Δ = 2496
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:

$\sqrt{\Delta}=\sqrt{2496}=\sqrt{64*39}=\sqrt{64}*\sqrt{39}=8\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-8\sqrt{39}}{2*-12}=\frac{-48-8\sqrt{39}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+8\sqrt{39}}{2*-12}=\frac{-48+8\sqrt{39}}{-24}
$