6y=5y(y+13)

Solution for 6y=5y(y+13) equation:

6y=5y(y+13)

We move all terms to the left:

6y-(5y(y+13))=0


We calculate terms in parentheses: -(5y(y+13)), so:

5y(y+13)

We multiply parentheses

5y^2+65y

Back to the equation:

-(5y^2+65y)


We get rid of parentheses

-5y^2+6y-65y=0

We add all the numbers together, and all the variables

-5y^2-59y=0

a = -5; b = -59; c = 0;
Δ = b2-4ac
Δ = -592-4·(-5)·0
Δ = 3481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3481}=59$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-59)-59}{2*-5}=\frac{0}{-10}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-59)+59}{2*-5}=\frac{118}{-10}
=-11+4/5
$