3(y+5)5y=2(y-6)

Solution for 3(y+5)5y=2(y-6) equation:

3(y+5)5y=2(y-6)

We move all terms to the left:

3(y+5)5y-(2(y-6))=0

We multiply parentheses

15y^2+75y-(2(y-6))=0


We calculate terms in parentheses: -(2(y-6)), so:

2(y-6)

We multiply parentheses

2y-12

Back to the equation:

-(2y-12)


We get rid of parentheses

15y^2+75y-2y+12=0

We add all the numbers together, and all the variables

15y^2+73y+12=0

a = 15; b = 73; c = +12;
Δ = b2-4ac
Δ = 732-4·15·12
Δ = 4609
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(73)-\sqrt{4609}}{2*15}=\frac{-73-\sqrt{4609}}{30}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(73)+\sqrt{4609}}{2*15}=\frac{-73+\sqrt{4609}}{30}
$