(x+3)(x+6)/2=119

Solution for (x+3)(x+6)/2=119 equation:

(x+3)(x+6)/2=119

We move all terms to the left:

(x+3)(x+6)/2-(119)=0

We multiply parentheses ..

(+x^2+6x+3x+18)/2-119=0

We multiply all the terms by the denominator


(+x^2+6x+3x+18)-119*2=0

We add all the numbers together, and all the variables

(+x^2+6x+3x+18)-238=0

We get rid of parentheses

x^2+6x+3x+18-238=0

We add all the numbers together, and all the variables

x^2+9x-220=0

a = 1; b = 9; c = -220;
Δ = b2-4ac
Δ = 92-4·1·(-220)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-31}{2*1}=\frac{-40}{2}
=-20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+31}{2*1}=\frac{22}{2}
=11
$