4x(2x-6)=6(2x+1)

Solution for 4x(2x-6)=6(2x+1) equation:

4x(2x-6)=6(2x+1)

We move all terms to the left:

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

We multiply parentheses

8x^2-24x-(6(2x+1))=0


We calculate terms in parentheses: -(6(2x+1)), so:

6(2x+1)

We multiply parentheses

12x+6

Back to the equation:

-(12x+6)


We get rid of parentheses

8x^2-24x-12x-6=0

We add all the numbers together, and all the variables

8x^2-36x-6=0

a = 8; b = -36; c = -6;
Δ = b2-4ac
Δ = -362-4·8·(-6)
Δ = 1488
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:

$\sqrt{\Delta}=\sqrt{1488}=\sqrt{16*93}=\sqrt{16}*\sqrt{93}=4\sqrt{93}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{93}}{2*8}=\frac{36-4\sqrt{93}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{93}}{2*8}=\frac{36+4\sqrt{93}}{16}
$