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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

(x+3)(x+21)-125=0

We multiply parentheses ..

(+x^2+21x+3x+63)-125=0

We get rid of parentheses

x^2+21x+3x+63-125=0

We add all the numbers together, and all the variables

x^2+24x-62=0

a = 1; b = 24; c = -62;
Δ = b2-4ac
Δ = 242-4·1·(-62)
Δ = 824
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{824}=\sqrt{4*206}=\sqrt{4}*\sqrt{206}=2\sqrt{206}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{206}}{2*1}=\frac{-24-2\sqrt{206}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{206}}{2*1}=\frac{-24+2\sqrt{206}}{2}
$