X(x+6)=8x(x+3)

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

X(X+6)=8X(X+3)

We move all terms to the left:

X(X+6)-(8X(X+3))=0

We multiply parentheses

X^2+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

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

We add all the numbers together, and all the variables

-7X^2-18X=0

a = -7; b = -18; c = 0;
Δ = b2-4ac
Δ = -182-4·(-7)·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-18}{2*-7}=\frac{0}{-14}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18}{2*-7}=\frac{36}{-14}
=-2+4/7
$