6x=8x(x-3)

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

6x=8x(x-3)

We move all terms to the left:

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


We calculate terms in parentheses: -(8x(x-3)), so:

8x(x-3)

We multiply parentheses

8x^2-24x

Back to the equation:

-(8x^2-24x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

-8x^2+30x=0

a = -8; b = 30; c = 0;
Δ = b2-4ac
Δ = 302-4·(-8)·0
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-30}{2*-8}=\frac{-60}{-16}
=3+3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+30}{2*-8}=\frac{0}{-16}
=0
$