80=(x+3)(x+5)

Solution for 80=(x+3)(x+5) equation:

80=(x+3)(x+5)

We move all terms to the left:

80-((x+3)(x+5))=0

We multiply parentheses ..

-((+x^2+5x+3x+15))+80=0


We calculate terms in parentheses: -((+x^2+5x+3x+15)), so:

(+x^2+5x+3x+15)

We get rid of parentheses

x^2+5x+3x+15

We add all the numbers together, and all the variables

x^2+8x+15

Back to the equation:

-(x^2+8x+15)


We get rid of parentheses

-x^2-8x-15+80=0

We add all the numbers together, and all the variables

-1x^2-8x+65=0

a = -1; b = -8; c = +65;
Δ = b2-4ac
Δ = -82-4·(-1)·65
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-18}{2*-1}=\frac{-10}{-2}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+18}{2*-1}=\frac{26}{-2}
=-13
$