1185=15+45x(x+2)

Solution for 1185=15+45x(x+2) equation:

1185=15+45x(x+2)

We move all terms to the left:

1185-(15+45x(x+2))=0


We calculate terms in parentheses: -(15+45x(x+2)), so:

15+45x(x+2)

determiningTheFunctionDomain
45x(x+2)+15

We multiply parentheses

45x^2+90x+15

Back to the equation:

-(45x^2+90x+15)


We get rid of parentheses

-45x^2-90x-15+1185=0

We add all the numbers together, and all the variables

-45x^2-90x+1170=0

a = -45; b = -90; c = +1170;
Δ = b2-4ac
Δ = -902-4·(-45)·1170
Δ = 218700
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:

$\sqrt{\Delta}=\sqrt{218700}=\sqrt{72900*3}=\sqrt{72900}*\sqrt{3}=270\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-270\sqrt{3}}{2*-45}=\frac{90-270\sqrt{3}}{-90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+270\sqrt{3}}{2*-45}=\frac{90+270\sqrt{3}}{-90}
$