(4w+9)(2w-5)-(3w+8)=0

Solution for (4w+9)(2w-5)-(3w+8)=0 equation:

(4w+9)(2w-5)-(3w+8)=0

We get rid of parentheses

(4w+9)(2w-5)-3w-8=0

We multiply parentheses ..

(+8w^2-20w+18w-45)-3w-8=0

We get rid of parentheses

8w^2-20w+18w-3w-45-8=0

We add all the numbers together, and all the variables

8w^2-5w-53=0

a = 8; b = -5; c = -53;
Δ = b2-4ac
Δ = -52-4·8·(-53)
Δ = 1721
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{-(-5)-\sqrt{1721}}{2*8}=\frac{5-\sqrt{1721}}{16}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{1721}}{2*8}=\frac{5+\sqrt{1721}}{16}
$