4x(x-2)=6(3x+2)

Solution for 4x(x-2)=6(3x+2) equation:

4x(x-2)=6(3x+2)

We move all terms to the left:

4x(x-2)-(6(3x+2))=0

We multiply parentheses

4x^2-8x-(6(3x+2))=0


We calculate terms in parentheses: -(6(3x+2)), so:

6(3x+2)

We multiply parentheses

18x+12

Back to the equation:

-(18x+12)


We get rid of parentheses

4x^2-8x-18x-12=0

We add all the numbers together, and all the variables

4x^2-26x-12=0

a = 4; b = -26; c = -12;
Δ = b2-4ac
Δ = -262-4·4·(-12)
Δ = 868
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:

$\sqrt{\Delta}=\sqrt{868}=\sqrt{4*217}=\sqrt{4}*\sqrt{217}=2\sqrt{217}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{217}}{2*4}=\frac{26-2\sqrt{217}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{217}}{2*4}=\frac{26+2\sqrt{217}}{8}
$