390=(x)+(x+30)+(x+30x2)

Solution for 390=(x)+(x+30)+(x+30x2) equation:

390=(x)+(x+30)+(x+30x^2)

We move all terms to the left:

390-((x)+(x+30)+(x+30x^2))=0


We calculate terms in parentheses: -(x+(x+30)+(x+30x^2)), so:

x+(x+30)+(x+30x^2)

determiningTheFunctionDomain
(x+30x^2)+x+(x+30)

We get rid of parentheses

30x^2+x+x+x+30

We add all the numbers together, and all the variables

30x^2+3x+30

Back to the equation:

-(30x^2+3x+30)


We get rid of parentheses

-30x^2-3x-30+390=0

We add all the numbers together, and all the variables

-30x^2-3x+360=0

a = -30; b = -3; c = +360;
Δ = b2-4ac
Δ = -32-4·(-30)·360
Δ = 43209
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:

$\sqrt{\Delta}=\sqrt{43209}=\sqrt{9*4801}=\sqrt{9}*\sqrt{4801}=3\sqrt{4801}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{4801}}{2*-30}=\frac{3-3\sqrt{4801}}{-60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{4801}}{2*-30}=\frac{3+3\sqrt{4801}}{-60}
$