4x(3x-1)=11x-3(x-4)

Solution for 4x(3x-1)=11x-3(x-4) equation:

4x(3x-1)=11x-3(x-4)

We move all terms to the left:

4x(3x-1)-(11x-3(x-4))=0

We multiply parentheses

12x^2-4x-(11x-3(x-4))=0


We calculate terms in parentheses: -(11x-3(x-4)), so:

11x-3(x-4)

We multiply parentheses

11x-3x+12

We add all the numbers together, and all the variables

8x+12

Back to the equation:

-(8x+12)


We get rid of parentheses

12x^2-4x-8x-12=0

We add all the numbers together, and all the variables

12x^2-12x-12=0

a = 12; b = -12; c = -12;
Δ = b2-4ac
Δ = -122-4·12·(-12)
Δ = 720
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:

$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12\sqrt{5}}{2*12}=\frac{12-12\sqrt{5}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12\sqrt{5}}{2*12}=\frac{12+12\sqrt{5}}{24}
$