6(6+9)=x(x+4)

Solution for 6(6+9)=x(x+4) equation:

6(6+9)=x(x+4)

We move all terms to the left:

6(6+9)-(x(x+4))=0

We add all the numbers together, and all the variables

-(x(x+4))+615=0


We calculate terms in parentheses: -(x(x+4)), so:

x(x+4)

We multiply parentheses

x^2+4x

Back to the equation:

-(x^2+4x)


We get rid of parentheses

-x^2-4x+615=0

We add all the numbers together, and all the variables

-1x^2-4x+615=0

a = -1; b = -4; c = +615;
Δ = b2-4ac
Δ = -42-4·(-1)·615
Δ = 2476
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:

$\sqrt{\Delta}=\sqrt{2476}=\sqrt{4*619}=\sqrt{4}*\sqrt{619}=2\sqrt{619}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{619}}{2*-1}=\frac{4-2\sqrt{619}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{619}}{2*-1}=\frac{4+2\sqrt{619}}{-2}
$