8y^2-30y+27=8y

Solution for 8y^2-30y+27=8y equation:

8y^2-30y+27=8y

We move all terms to the left:

8y^2-30y+27-(8y)=0

We add all the numbers together, and all the variables

8y^2-38y+27=0

a = 8; b = -38; c = +27;
Δ = b2-4ac
Δ = -382-4·8·27
Δ = 580
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:

$\sqrt{\Delta}=\sqrt{580}=\sqrt{4*145}=\sqrt{4}*\sqrt{145}=2\sqrt{145}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-2\sqrt{145}}{2*8}=\frac{38-2\sqrt{145}}{16}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+2\sqrt{145}}{2*8}=\frac{38+2\sqrt{145}}{16}
$