3(y+5)9y=45

Solution for 3(y+5)9y=45 equation:

3(y+5)9y=45

We move all terms to the left:

3(y+5)9y-(45)=0

We multiply parentheses

27y^2+135y-45=0

a = 27; b = 135; c = -45;
Δ = b2-4ac
Δ = 1352-4·27·(-45)
Δ = 23085
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{23085}=\sqrt{81*285}=\sqrt{81}*\sqrt{285}=9\sqrt{285}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(135)-9\sqrt{285}}{2*27}=\frac{-135-9\sqrt{285}}{54}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(135)+9\sqrt{285}}{2*27}=\frac{-135+9\sqrt{285}}{54}
$