4(w-3)1w=1w-6

Solution for 4(w-3)1w=1w-6 equation:

4(w-3)1w=1w-6

We move all terms to the left:

4(w-3)1w-(1w-6)=0

We add all the numbers together, and all the variables

4(w-3)1w-(w-6)=0

We multiply parentheses

4w^2-12w-(w-6)=0

We get rid of parentheses

4w^2-12w-w+6=0

We add all the numbers together, and all the variables

4w^2-13w+6=0

a = 4; b = -13; c = +6;
Δ = b2-4ac
Δ = -132-4·4·6
Δ = 73
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{-(-13)-\sqrt{73}}{2*4}=\frac{13-\sqrt{73}}{8}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{73}}{2*4}=\frac{13+\sqrt{73}}{8}
$