(x+3)(x+12)=12(x+18)

Solution for (x+3)(x+12)=12(x+18) equation:

(x+3)(x+12)=12(x+18)

We move all terms to the left:

(x+3)(x+12)-(12(x+18))=0

We multiply parentheses ..

(+x^2+12x+3x+36)-(12(x+18))=0


We calculate terms in parentheses: -(12(x+18)), so:

12(x+18)

We multiply parentheses

12x+216

Back to the equation:

-(12x+216)


We get rid of parentheses

x^2+12x+3x-12x+36-216=0

We add all the numbers together, and all the variables

x^2+3x-180=0

a = 1; b = 3; c = -180;
Δ = b2-4ac
Δ = 32-4·1·(-180)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-27}{2*1}=\frac{-30}{2}
=-15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+27}{2*1}=\frac{24}{2}
=12
$