(Y-4)^2=2y^2-15y+22

Solution for (Y-4)^2=2y^2-15y+22 equation:

(-4)^2=2Y^2-15Y+22

We move all terms to the left:

(-4)^2-(2Y^2-15Y+22)=0

We add all the numbers together, and all the variables

-(2Y^2-15Y+22)+16=0

We get rid of parentheses

-2Y^2+15Y-22+16=0

We add all the numbers together, and all the variables

-2Y^2+15Y-6=0

a = -2; b = 15; c = -6;
Δ = b2-4ac
Δ = 152-4·(-2)·(-6)
Δ = 177
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{-(15)-\sqrt{177}}{2*-2}=\frac{-15-\sqrt{177}}{-4}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{177}}{2*-2}=\frac{-15+\sqrt{177}}{-4}
$