30+x=3x(4+x)

Solution for 30+x=3x(4+x) equation:

30+x=3x(4+x)

We move all terms to the left:

30+x-(3x(4+x))=0

We add all the numbers together, and all the variables

x-(3x(x+4))+30=0


We calculate terms in parentheses: -(3x(x+4)), so:

3x(x+4)

We multiply parentheses

3x^2+12x

Back to the equation:

-(3x^2+12x)


We get rid of parentheses

-3x^2+x-12x+30=0

We add all the numbers together, and all the variables

-3x^2-11x+30=0

a = -3; b = -11; c = +30;
Δ = b2-4ac
Δ = -112-4·(-3)·30
Δ = 481
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{481}}{2*-3}=\frac{11-\sqrt{481}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{481}}{2*-3}=\frac{11+\sqrt{481}}{-6}
$