5x+15+4x=6x-3x(x+9)

Solution for 5x+15+4x=6x-3x(x+9) equation:

5x+15+4x=6x-3x(x+9)

We move all terms to the left:

5x+15+4x-(6x-3x(x+9))=0

We add all the numbers together, and all the variables

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


We calculate terms in parentheses: -(6x-3x(x+9)), so:

6x-3x(x+9)

We multiply parentheses

-3x^2+6x-27x

We add all the numbers together, and all the variables

-3x^2-21x

Back to the equation:

-(-3x^2-21x)


We get rid of parentheses

3x^2+21x+9x+15=0

We add all the numbers together, and all the variables

3x^2+30x+15=0

a = 3; b = 30; c = +15;
Δ = b2-4ac
Δ = 302-4·3·15
Δ = 720
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:

$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-12\sqrt{5}}{2*3}=\frac{-30-12\sqrt{5}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+12\sqrt{5}}{2*3}=\frac{-30+12\sqrt{5}}{6}
$