15w(2w+3)+2w=10w+17w

Solution for 15w(2w+3)+2w=10w+17w equation:

15w(2w+3)+2w=10w+17w

We move all terms to the left:

15w(2w+3)+2w-(10w+17w)=0

We add all the numbers together, and all the variables

15w(2w+3)+2w-(+27w)=0

We add all the numbers together, and all the variables

2w+15w(2w+3)-(+27w)=0

We multiply parentheses

30w^2+2w+45w-(+27w)=0

We get rid of parentheses

30w^2+2w+45w-27w=0

We add all the numbers together, and all the variables

30w^2+20w=0

a = 30; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·30·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*30}=\frac{-40}{60}
=-2/3
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*30}=\frac{0}{60}
=0
$