(=3w-8)(3w-5)

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

(=3w-8)(3w-5)

We move all terms to the left:

(-(3w-8)(3w-5))=0

We multiply parentheses ..

(-(+9w^2-15w-24w+40))=0


We calculate terms in parentheses: +(-(+9w^2-15w-24w+40)), so:

-(+9w^2-15w-24w+40)

We get rid of parentheses

-9w^2+15w+24w-40

We add all the numbers together, and all the variables

-9w^2+39w-40

Back to the equation:

+(-9w^2+39w-40)


We get rid of parentheses

-9w^2+39w-40=0

a = -9; b = 39; c = -40;
Δ = b2-4ac
Δ = 392-4·(-9)·(-40)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(39)-9}{2*-9}=\frac{-48}{-18}
=2+2/3
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+9}{2*-9}=\frac{-30}{-18}
=1+2/3
$