-7w(w+1)=-9w-27

Solution for -7w(w+1)=-9w-27 equation:

-7w(w+1)=-9w-27

We move all terms to the left:

-7w(w+1)-(-9w-27)=0

We multiply parentheses

-7w^2-7w-(-9w-27)=0

We get rid of parentheses

-7w^2-7w+9w+27=0

We add all the numbers together, and all the variables

-7w^2+2w+27=0

a = -7; b = 2; c = +27;
Δ = b2-4ac
Δ = 22-4·(-7)·27
Δ = 760
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:

$\sqrt{\Delta}=\sqrt{760}=\sqrt{4*190}=\sqrt{4}*\sqrt{190}=2\sqrt{190}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{190}}{2*-7}=\frac{-2-2\sqrt{190}}{-14}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{190}}{2*-7}=\frac{-2+2\sqrt{190}}{-14}
$