6(x-2)+18=2(x-3)x

Solution for 6(x-2)+18=2(x-3)x equation:

6(x-2)+18=2(x-3)x

We move all terms to the left:

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

We multiply parentheses

6x-(2(x-3)x)-12+18=0


We calculate terms in parentheses: -(2(x-3)x), so:

2(x-3)x

We multiply parentheses

2x^2-6x

Back to the equation:

-(2x^2-6x)


We add all the numbers together, and all the variables

6x-(2x^2-6x)+6=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

-2x^2+12x+6=0

a = -2; b = 12; c = +6;
Δ = b2-4ac
Δ = 122-4·(-2)·6
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-8\sqrt{3}}{2*-2}=\frac{-12-8\sqrt{3}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+8\sqrt{3}}{2*-2}=\frac{-12+8\sqrt{3}}{-4}
$