(2w+1)(w+6)=5

Solution for (2w+1)(w+6)=5 equation:

(2w+1)(w+6)=5

We move all terms to the left:

(2w+1)(w+6)-(5)=0

We multiply parentheses ..

(+2w^2+12w+w+6)-5=0

We get rid of parentheses

2w^2+12w+w+6-5=0

We add all the numbers together, and all the variables

2w^2+13w+1=0

a = 2; b = 13; c = +1;
Δ = b2-4ac
Δ = 132-4·2·1
Δ = 161
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-\sqrt{161}}{2*2}=\frac{-13-\sqrt{161}}{4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{161}}{2*2}=\frac{-13+\sqrt{161}}{4}
$