6x(x-8)=7x(x-3)

Solution for 6x(x-8)=7x(x-3) equation:

6x(x-8)=7x(x-3)

We move all terms to the left:

6x(x-8)-(7x(x-3))=0

We multiply parentheses

6x^2-48x-(7x(x-3))=0


We calculate terms in parentheses: -(7x(x-3)), so:

7x(x-3)

We multiply parentheses

7x^2-21x

Back to the equation:

-(7x^2-21x)


We get rid of parentheses

6x^2-7x^2-48x+21x=0

We add all the numbers together, and all the variables

-1x^2-27x=0

a = -1; b = -27; c = 0;
Δ = b2-4ac
Δ = -272-4·(-1)·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-27}{2*-1}=\frac{0}{-2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+27}{2*-1}=\frac{54}{-2}
=-27
$