(6+x)(11+x)=28

Solution for (6+x)(11+x)=28 equation:

(6+x)(11+x)=28

We move all terms to the left:

(6+x)(11+x)-(28)=0

We add all the numbers together, and all the variables

(x+6)(x+11)-28=0

We multiply parentheses ..

(+x^2+11x+6x+66)-28=0

We get rid of parentheses

x^2+11x+6x+66-28=0

We add all the numbers together, and all the variables

x^2+17x+38=0

a = 1; b = 17; c = +38;
Δ = b2-4ac
Δ = 172-4·1·38
Δ = 137
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-\sqrt{137}}{2*1}=\frac{-17-\sqrt{137}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+\sqrt{137}}{2*1}=\frac{-17+\sqrt{137}}{2}
$