(6+2w)(5+2w)=100

Solution for (6+2w)(5+2w)=100 equation:

(6+2w)(5+2w)=100

We move all terms to the left:

(6+2w)(5+2w)-(100)=0

We add all the numbers together, and all the variables

(2w+6)(2w+5)-100=0

We multiply parentheses ..

(+4w^2+10w+12w+30)-100=0

We get rid of parentheses

4w^2+10w+12w+30-100=0

We add all the numbers together, and all the variables

4w^2+22w-70=0

a = 4; b = 22; c = -70;
Δ = b2-4ac
Δ = 222-4·4·(-70)
Δ = 1604
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1604}=\sqrt{4*401}=\sqrt{4}*\sqrt{401}=2\sqrt{401}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{401}}{2*4}=\frac{-22-2\sqrt{401}}{8}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{401}}{2*4}=\frac{-22+2\sqrt{401}}{8}
$