x(27-x)+(x-(27-x))=183

Solution for x(27-x)+(x-(27-x))=183 equation:

x(27-x)+(x-(27-x))=183

We move all terms to the left:

x(27-x)+(x-(27-x))-(183)=0

We add all the numbers together, and all the variables

x(-1x+27)+(x-(-1x+27))-183=0

We multiply parentheses

-1x^2+27x+(x-(-1x+27))-183=0


We calculate terms in parentheses: +(x-(-1x+27)), so:

x-(-1x+27)

We get rid of parentheses

x+1x-27

We add all the numbers together, and all the variables

2x-27

Back to the equation:

+(2x-27)


We get rid of parentheses

-1x^2+27x+2x-27-183=0

We add all the numbers together, and all the variables

-1x^2+29x-210=0

a = -1; b = 29; c = -210;
Δ = b2-4ac
Δ = 292-4·(-1)·(-210)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-1}{2*-1}=\frac{-30}{-2}
=+15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+1}{2*-1}=\frac{-28}{-2}
=+14
$