(Y-2)^2=2y^2-13y+24

Solution for (Y-2)^2=2y^2-13y+24 equation:

(-2)^2=2Y^2-13Y+24

We move all terms to the left:

(-2)^2-(2Y^2-13Y+24)=0

We add all the numbers together, and all the variables

-(2Y^2-13Y+24)+4=0

We get rid of parentheses

-2Y^2+13Y-24+4=0

We add all the numbers together, and all the variables

-2Y^2+13Y-20=0

a = -2; b = 13; c = -20;
Δ = b2-4ac
Δ = 132-4·(-2)·(-20)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-3}{2*-2}=\frac{-16}{-4}
=+4
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+3}{2*-2}=\frac{-10}{-4}
=2+1/2
$