(x)(-x.6)+18=6(x+3)

Solution for (x)(-x.6)+18=6(x+3) equation:

(x)(-x.6)+18=6(x+3)

We move all terms to the left:

(x)(-x.6)+18-(6(x+3))=0

We multiply parentheses

-1x^2-(6(x+3))+18=0


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

6(x+3)

We multiply parentheses

6x+18

Back to the equation:

-(6x+18)


We get rid of parentheses

-1x^2-6x-18+18=0

We add all the numbers together, and all the variables

-1x^2-6x=0

a = -1; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·(-1)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*-1}=\frac{0}{-2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*-1}=\frac{12}{-2}
=-6
$