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

Solution for x(x-3)=2(x+12) equation:

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

We move all terms to the left:

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

We multiply parentheses

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


We calculate terms in parentheses: -(2(x+12)), so:

2(x+12)

We multiply parentheses

2x+24

Back to the equation:

-(2x+24)


We get rid of parentheses

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

We add all the numbers together, and all the variables

x^2-5x-24=0

a = 1; b = -5; c = -24;
Δ = b2-4ac
Δ = -52-4·1·(-24)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-11}{2*1}=\frac{-6}{2}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+11}{2*1}=\frac{16}{2}
=8
$