(x+5)=x(3x+12)

Solution for (x+5)=x(3x+12) equation:

(x+5)=x(3x+12)

We move all terms to the left:

(x+5)-(x(3x+12))=0

We get rid of parentheses

x-(x(3x+12))+5=0


We calculate terms in parentheses: -(x(3x+12)), so:

x(3x+12)

We multiply parentheses

3x^2+12x

Back to the equation:

-(3x^2+12x)


We get rid of parentheses

-3x^2+x-12x+5=0

We add all the numbers together, and all the variables

-3x^2-11x+5=0

a = -3; b = -11; c = +5;
Δ = b2-4ac
Δ = -112-4·(-3)·5
Δ = 181
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-\sqrt{181}}{2*-3}=\frac{11-\sqrt{181}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{181}}{2*-3}=\frac{11+\sqrt{181}}{-6}
$