(x+5)(x+21)=13(x+13)

Solution for (x+5)(x+21)=13(x+13) equation:

(x+5)(x+21)=13(x+13)

We move all terms to the left:

(x+5)(x+21)-(13(x+13))=0

We multiply parentheses ..

(+x^2+21x+5x+105)-(13(x+13))=0


We calculate terms in parentheses: -(13(x+13)), so:

13(x+13)

We multiply parentheses

13x+169

Back to the equation:

-(13x+169)


We get rid of parentheses

x^2+21x+5x-13x+105-169=0

We add all the numbers together, and all the variables

x^2+13x-64=0

a = 1; b = 13; c = -64;
Δ = b2-4ac
Δ = 132-4·1·(-64)
Δ = 425
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:

$\sqrt{\Delta}=\sqrt{425}=\sqrt{25*17}=\sqrt{25}*\sqrt{17}=5\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-5\sqrt{17}}{2*1}=\frac{-13-5\sqrt{17}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+5\sqrt{17}}{2*1}=\frac{-13+5\sqrt{17}}{2}
$