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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

(3w+8)(2w-14)=0

We multiply parentheses ..

(+6w^2-42w+16w-112)=0

We get rid of parentheses

6w^2-42w+16w-112=0

We add all the numbers together, and all the variables

6w^2-26w-112=0

a = 6; b = -26; c = -112;
Δ = b2-4ac
Δ = -262-4·6·(-112)
Δ = 3364
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3364}=58$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-58}{2*6}=\frac{-32}{12}
=-2+2/3
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+58}{2*6}=\frac{84}{12}
=7
$