3(x-2)=4x(x+8)

Solution for 3(x-2)=4x(x+8) equation:

3(x-2)=4x(x+8)

We move all terms to the left:

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

We multiply parentheses

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


We calculate terms in parentheses: -(4x(x+8)), so:

4x(x+8)

We multiply parentheses

4x^2+32x

Back to the equation:

-(4x^2+32x)


We get rid of parentheses

-4x^2+3x-32x-6=0

We add all the numbers together, and all the variables

-4x^2-29x-6=0

a = -4; b = -29; c = -6;
Δ = b2-4ac
Δ = -292-4·(-4)·(-6)
Δ = 745
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{-(-29)-\sqrt{745}}{2*-4}=\frac{29-\sqrt{745}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+\sqrt{745}}{2*-4}=\frac{29+\sqrt{745}}{-8}
$