-2w(w+10)=6w+12

Solution for -2w(w+10)=6w+12 equation:

-2w(w+10)=6w+12

We move all terms to the left:

-2w(w+10)-(6w+12)=0

We multiply parentheses

-2w^2-20w-(6w+12)=0

We get rid of parentheses

-2w^2-20w-6w-12=0

We add all the numbers together, and all the variables

-2w^2-26w-12=0

a = -2; b = -26; c = -12;
Δ = b2-4ac
Δ = -262-4·(-2)·(-12)
Δ = 580
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:

$\sqrt{\Delta}=\sqrt{580}=\sqrt{4*145}=\sqrt{4}*\sqrt{145}=2\sqrt{145}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{145}}{2*-2}=\frac{26-2\sqrt{145}}{-4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{145}}{2*-2}=\frac{26+2\sqrt{145}}{-4}
$