(x+9)(x+12)=238

Solution for (x+9)(x+12)=238 equation:

(x+9)(x+12)=238

We move all terms to the left:

(x+9)(x+12)-(238)=0

We multiply parentheses ..

(+x^2+12x+9x+108)-238=0

We get rid of parentheses

x^2+12x+9x+108-238=0

We add all the numbers together, and all the variables

x^2+21x-130=0

a = 1; b = 21; c = -130;
Δ = b2-4ac
Δ = 212-4·1·(-130)
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{-(21)-31}{2*1}=\frac{-52}{2}
=-26
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+31}{2*1}=\frac{10}{2}
=5
$