34-4w(2w+1)=10w-4(10+w)

Solution for 34-4w(2w+1)=10w-4(10+w) equation:

34-4w(2w+1)=10w-4(10+w)

We move all terms to the left:

34-4w(2w+1)-(10w-4(10+w))=0

We add all the numbers together, and all the variables

-4w(2w+1)-(10w-4(w+10))+34=0

We multiply parentheses

-8w^2-4w-(10w-4(w+10))+34=0


We calculate terms in parentheses: -(10w-4(w+10)), so:

10w-4(w+10)

We multiply parentheses

10w-4w-40

We add all the numbers together, and all the variables

6w-40

Back to the equation:

-(6w-40)


We get rid of parentheses

-8w^2-4w-6w+40+34=0

We add all the numbers together, and all the variables

-8w^2-10w+74=0

a = -8; b = -10; c = +74;
Δ = b2-4ac
Δ = -102-4·(-8)·74
Δ = 2468
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2468}=\sqrt{4*617}=\sqrt{4}*\sqrt{617}=2\sqrt{617}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{617}}{2*-8}=\frac{10-2\sqrt{617}}{-16}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{617}}{2*-8}=\frac{10+2\sqrt{617}}{-16}
$