(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 multiply parentheses ..

(+6w^2-27w+16w-72)-5=0

We get rid of parentheses

6w^2-27w+16w-72-5=0

We add all the numbers together, and all the variables

6w^2-11w-77=0

a = 6; b = -11; c = -77;
Δ = b2-4ac
Δ = -112-4·6·(-77)
Δ = 1969
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{-(-11)-\sqrt{1969}}{2*6}=\frac{11-\sqrt{1969}}{12}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{1969}}{2*6}=\frac{11+\sqrt{1969}}{12}
$