6y^2=14-40y

Solution for 6y^2=14-40y equation:

6y^2=14-40y

We move all terms to the left:

6y^2-(14-40y)=0

We add all the numbers together, and all the variables

6y^2-(-40y+14)=0

We get rid of parentheses

6y^2+40y-14=0

a = 6; b = 40; c = -14;
Δ = b2-4ac
Δ = 402-4·6·(-14)
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-44}{2*6}=\frac{-84}{12}
=-7
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+44}{2*6}=\frac{4}{12}
=1/3
$