3(x+1)+9=2(x+6)x

Solution for 3(x+1)+9=2(x+6)x equation:

3(x+1)+9=2(x+6)x

We move all terms to the left:

3(x+1)+9-(2(x+6)x)=0

We multiply parentheses

3x-(2(x+6)x)+3+9=0


We calculate terms in parentheses: -(2(x+6)x), so:

2(x+6)x

We multiply parentheses

2x^2+12x

Back to the equation:

-(2x^2+12x)


We add all the numbers together, and all the variables

3x-(2x^2+12x)+12=0

We get rid of parentheses

-2x^2+3x-12x+12=0

We add all the numbers together, and all the variables

-2x^2-9x+12=0

a = -2; b = -9; c = +12;
Δ = b2-4ac
Δ = -92-4·(-2)·12
Δ = 177
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{177}}{2*-2}=\frac{9-\sqrt{177}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{177}}{2*-2}=\frac{9+\sqrt{177}}{-4}
$