-3(2w+5)+7w=5w(w-11)

Solution for -3(2w+5)+7w=5w(w-11) equation:

-3(2w+5)+7w=5w(w-11)

We move all terms to the left:

-3(2w+5)+7w-(5w(w-11))=0

We add all the numbers together, and all the variables

7w-3(2w+5)-(5w(w-11))=0

We multiply parentheses

7w-6w-(5w(w-11))-15=0


We calculate terms in parentheses: -(5w(w-11)), so:

5w(w-11)

We multiply parentheses

5w^2-55w

Back to the equation:

-(5w^2-55w)


We add all the numbers together, and all the variables

w-(5w^2-55w)-15=0

We get rid of parentheses

-5w^2+w+55w-15=0

We add all the numbers together, and all the variables

-5w^2+56w-15=0

a = -5; b = 56; c = -15;
Δ = b2-4ac
Δ = 562-4·(-5)·(-15)
Δ = 2836
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:

$\sqrt{\Delta}=\sqrt{2836}=\sqrt{4*709}=\sqrt{4}*\sqrt{709}=2\sqrt{709}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-2\sqrt{709}}{2*-5}=\frac{-56-2\sqrt{709}}{-10}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+2\sqrt{709}}{2*-5}=\frac{-56+2\sqrt{709}}{-10}
$