3(x-8)=x(x+15)

Solution for 3(x-8)=x(x+15) equation:

3(x-8)=x(x+15)

We move all terms to the left:

3(x-8)-(x(x+15))=0

We multiply parentheses

3x-(x(x+15))-24=0


We calculate terms in parentheses: -(x(x+15)), so:

x(x+15)

We multiply parentheses

x^2+15x

Back to the equation:

-(x^2+15x)


We get rid of parentheses

-x^2+3x-15x-24=0

We add all the numbers together, and all the variables

-1x^2-12x-24=0

a = -1; b = -12; c = -24;
Δ = b2-4ac
Δ = -122-4·(-1)·(-24)
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{3}}{2*-1}=\frac{12-4\sqrt{3}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{3}}{2*-1}=\frac{12+4\sqrt{3}}{-2}
$