229=x(3x+5)+(11+x)+18

Solution for 229=x(3x+5)+(11+x)+18 equation:

229=x(3x+5)+(11+x)+18

We move all terms to the left:

229-(x(3x+5)+(11+x)+18)=0

We add all the numbers together, and all the variables

-(x(3x+5)+(x+11)+18)+229=0


We calculate terms in parentheses: -(x(3x+5)+(x+11)+18), so:

x(3x+5)+(x+11)+18

We multiply parentheses

3x^2+5x+(x+11)+18

We get rid of parentheses

3x^2+5x+x+11+18

We add all the numbers together, and all the variables

3x^2+6x+29

Back to the equation:

-(3x^2+6x+29)


We get rid of parentheses

-3x^2-6x-29+229=0

We add all the numbers together, and all the variables

-3x^2-6x+200=0

a = -3; b = -6; c = +200;
Δ = b2-4ac
Δ = -62-4·(-3)·200
Δ = 2436
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:

$\sqrt{\Delta}=\sqrt{2436}=\sqrt{4*609}=\sqrt{4}*\sqrt{609}=2\sqrt{609}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{609}}{2*-3}=\frac{6-2\sqrt{609}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{609}}{2*-3}=\frac{6+2\sqrt{609}}{-6}
$