4(2x-1)(2x-1)-2x(2x-3)=11x^-4

Solution for 4(2x-1)(2x-1)-2x(2x-3)=11x^-4 equation:

4(2x-1)(2x-1)-2x(2x-3)=11x^-4

We move all terms to the left:

4(2x-1)(2x-1)-2x(2x-3)-(11x^-4)=0

We multiply parentheses

-4x^2+4(2x-1)(2x-1)+6x-(11x^-4)=0

We get rid of parentheses

-4x^2+4(2x-1)(2x-1)+6x-11x^+4=0

We multiply parentheses ..

-4x^2+4(+4x^2-2x-2x+1)+6x-11x^+4=0

We add all the numbers together, and all the variables

-4x^2+4(+4x^2-2x-2x+1)-5x+4=0

We multiply parentheses

-4x^2+16x^2-8x-8x-5x+4+4=0

We add all the numbers together, and all the variables

12x^2-21x+8=0

a = 12; b = -21; c = +8;
Δ = b2-4ac
Δ = -212-4·12·8
Δ = 57
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{-(-21)-\sqrt{57}}{2*12}=\frac{21-\sqrt{57}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{57}}{2*12}=\frac{21+\sqrt{57}}{24}
$