3w^2-w=234

Solution for 3w^2-w=234 equation:

3w^2-w=234

We move all terms to the left:

3w^2-w-(234)=0

We add all the numbers together, and all the variables

3w^2-1w-234=0

a = 3; b = -1; c = -234;
Δ = b2-4ac
Δ = -12-4·3·(-234)
Δ = 2809
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2809}=53$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-53}{2*3}=\frac{-52}{6}
=-8+2/3
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+53}{2*3}=\frac{54}{6}
=9
$