2(x+8)=3x(x-6)

Solution for 2(x+8)=3x(x-6) equation:

2(x+8)=3x(x-6)

We move all terms to the left:

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

We multiply parentheses

2x-(3x(x-6))+16=0


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

3x(x-6)

We multiply parentheses

3x^2-18x

Back to the equation:

-(3x^2-18x)


We get rid of parentheses

-3x^2+2x+18x+16=0

We add all the numbers together, and all the variables

-3x^2+20x+16=0

a = -3; b = 20; c = +16;
Δ = b2-4ac
Δ = 202-4·(-3)·16
Δ = 592
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:

$\sqrt{\Delta}=\sqrt{592}=\sqrt{16*37}=\sqrt{16}*\sqrt{37}=4\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{37}}{2*-3}=\frac{-20-4\sqrt{37}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{37}}{2*-3}=\frac{-20+4\sqrt{37}}{-6}
$