-1/2w+5=6w+18

Solution for -1/2w+5=6w+18 equation:

-1/2w+5=6w+18

We move all terms to the left:

-1/2w+5-(6w+18)=0


Domain of the equation: 2w!=0

w!=0/2

w!=0

w∈R


We get rid of parentheses

-1/2w-6w-18+5=0

We multiply all the terms by the denominator


-6w*2w-18*2w+5*2w-1=0

Wy multiply elements

-12w^2-36w+10w-1=0

We add all the numbers together, and all the variables

-12w^2-26w-1=0

a = -12; b = -26; c = -1;
Δ = b2-4ac
Δ = -262-4·(-12)·(-1)
Δ = 628
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:

$\sqrt{\Delta}=\sqrt{628}=\sqrt{4*157}=\sqrt{4}*\sqrt{157}=2\sqrt{157}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{157}}{2*-12}=\frac{26-2\sqrt{157}}{-24}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{157}}{2*-12}=\frac{26+2\sqrt{157}}{-24}
$