(x+3)(x+21)=3^5

Solution for (x+3)(x+21)=3^5 equation:

(x+3)(x+21)=3^5

We move all terms to the left:

(x+3)(x+21)-(3^5)=0

We add all the numbers together, and all the variables

(x+3)(x+21)-243=0

We multiply parentheses ..

(+x^2+21x+3x+63)-243=0

We get rid of parentheses

x^2+21x+3x+63-243=0

We add all the numbers together, and all the variables

x^2+24x-180=0

a = 1; b = 24; c = -180;
Δ = b2-4ac
Δ = 242-4·1·(-180)
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-36}{2*1}=\frac{-60}{2}
=-30
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+36}{2*1}=\frac{12}{2}
=6
$