5y(y+4)=6y

Solution for 5y(y+4)=6y equation:

5y(y+4)=6y

We move all terms to the left:

5y(y+4)-(6y)=0

We add all the numbers together, and all the variables

-6y+5y(y+4)=0

We multiply parentheses

5y^2-6y+20y=0

We add all the numbers together, and all the variables

5y^2+14y=0

a = 5; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·5·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*5}=\frac{-28}{10}
=-2+4/5
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*5}=\frac{0}{10}
=0
$