6y^2-y-40=0

Solution for 6y^2-y-40=0 equation:

6y^2-y-40=0

We add all the numbers together, and all the variables

6y^2-1y-40=0

a = 6; b = -1; c = -40;
Δ = b2-4ac
Δ = -12-4·6·(-40)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-31}{2*6}=\frac{-30}{12}
=-2+1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+31}{2*6}=\frac{32}{12}
=2+2/3
$