6y^2-y=48

Solution for 6y^2-y=48 equation:

6y^2-y=48

We move all terms to the left:

6y^2-y-(48)=0

We add all the numbers together, and all the variables

6y^2-1y-48=0

a = 6; b = -1; c = -48;
Δ = b2-4ac
Δ = -12-4·6·(-48)
Δ = 1153
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{1153}}{2*6}=\frac{1-\sqrt{1153}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{1153}}{2*6}=\frac{1+\sqrt{1153}}{12}
$