6w^2=w+6

Solution for 6w^2=w+6 equation:

6w^2=w+6

We move all terms to the left:

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

We get rid of parentheses

6w^2-w-6=0

We add all the numbers together, and all the variables

6w^2-1w-6=0

a = 6; b = -1; c = -6;
Δ = b2-4ac
Δ = -12-4·6·(-6)
Δ = 145
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{145}}{2*6}=\frac{1-\sqrt{145}}{12}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{145}}{2*6}=\frac{1+\sqrt{145}}{12}
$