(Y-5)^2=2y^2-11y+5

Solution for (Y-5)^2=2y^2-11y+5 equation:

(-5)^2=2Y^2-11Y+5

We move all terms to the left:

(-5)^2-(2Y^2-11Y+5)=0

We add all the numbers together, and all the variables

-(2Y^2-11Y+5)+25=0

We get rid of parentheses

-2Y^2+11Y-5+25=0

We add all the numbers together, and all the variables

-2Y^2+11Y+20=0

a = -2; b = 11; c = +20;
Δ = b2-4ac
Δ = 112-4·(-2)·20
Δ = 281
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{-(11)-\sqrt{281}}{2*-2}=\frac{-11-\sqrt{281}}{-4}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{281}}{2*-2}=\frac{-11+\sqrt{281}}{-4}
$