3(x-5)+6=x(-9-2x)

Solution for 3(x-5)+6=x(-9-2x) equation:

3(x-5)+6=x(-9-2x)

We move all terms to the left:

3(x-5)+6-(x(-9-2x))=0

We add all the numbers together, and all the variables

3(x-5)-(x(-2x-9))+6=0

We multiply parentheses

3x-(x(-2x-9))-15+6=0


We calculate terms in parentheses: -(x(-2x-9)), so:

x(-2x-9)

We multiply parentheses

-2x^2-9x

Back to the equation:

-(-2x^2-9x)


We add all the numbers together, and all the variables

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

We get rid of parentheses

2x^2+9x+3x-9=0

We add all the numbers together, and all the variables

2x^2+12x-9=0

a = 2; b = 12; c = -9;
Δ = b2-4ac
Δ = 122-4·2·(-9)
Δ = 216
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:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-6\sqrt{6}}{2*2}=\frac{-12-6\sqrt{6}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+6\sqrt{6}}{2*2}=\frac{-12+6\sqrt{6}}{4}
$