5(y-3)2y=27

Solution for 5(y-3)2y=27 equation:

5(y-3)2y=27

We move all terms to the left:

5(y-3)2y-(27)=0

We multiply parentheses

10y^2-30y-27=0

a = 10; b = -30; c = -27;
Δ = b2-4ac
Δ = -302-4·10·(-27)
Δ = 1980
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:

$\sqrt{\Delta}=\sqrt{1980}=\sqrt{36*55}=\sqrt{36}*\sqrt{55}=6\sqrt{55}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-6\sqrt{55}}{2*10}=\frac{30-6\sqrt{55}}{20}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+6\sqrt{55}}{2*10}=\frac{30+6\sqrt{55}}{20}
$