6y^2-5y=14

Solution for 6y^2-5y=14 equation:

6y^2-5y=14

We move all terms to the left:

6y^2-5y-(14)=0

a = 6; b = -5; c = -14;
Δ = b2-4ac
Δ = -52-4·6·(-14)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-19}{2*6}=\frac{-14}{12}
=-1+1/6
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+19}{2*6}=\frac{24}{12}
=2
$