5w(2w+3)+2w=10w2+17w2

Solution for 5w(2w+3)+2w=10w2+17w2 equation:

5w(2w+3)+2w=10w^2+17w^2

We move all terms to the left:

5w(2w+3)+2w-(10w^2+17w^2)=0

We add all the numbers together, and all the variables

-(10w^2+17w^2)+2w+5w(2w+3)=0

We multiply parentheses

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

We get rid of parentheses

-10w^2-17w^2+10w^2+2w+15w=0

We add all the numbers together, and all the variables

-17w^2+17w=0

a = -17; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·(-17)·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*-17}=\frac{-34}{-34}
=1
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*-17}=\frac{0}{-34}
=0
$