(4w-9)(w+2)=-14

Solution for (4w-9)(w+2)=-14 equation:

(4w-9)(w+2)=-14

We move all terms to the left:

(4w-9)(w+2)-(-14)=0

We add all the numbers together, and all the variables

(4w-9)(w+2)+14=0

We multiply parentheses ..

(+4w^2+8w-9w-18)+14=0

We get rid of parentheses

4w^2+8w-9w-18+14=0

We add all the numbers together, and all the variables

4w^2-1w-4=0

a = 4; b = -1; c = -4;
Δ = b2-4ac
Δ = -12-4·4·(-4)
Δ = 65
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{-(-1)-\sqrt{65}}{2*4}=\frac{1-\sqrt{65}}{8}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{65}}{2*4}=\frac{1+\sqrt{65}}{8}
$