(2w+5)(4w+1)=180

Solution for (2w+5)(4w+1)=180 equation:

(2w+5)(4w+1)=180

We move all terms to the left:

(2w+5)(4w+1)-(180)=0

We multiply parentheses ..

(+8w^2+2w+20w+5)-180=0

We get rid of parentheses

8w^2+2w+20w+5-180=0

We add all the numbers together, and all the variables

8w^2+22w-175=0

a = 8; b = 22; c = -175;
Δ = b2-4ac
Δ = 222-4·8·(-175)
Δ = 6084
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6084}=78$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-78}{2*8}=\frac{-100}{16}
=-6+1/4
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+78}{2*8}=\frac{56}{16}
=3+1/2
$