Y-4y+10=y(y-5)

Solution for Y-4y+10=y(y-5) equation:

-4Y+10=Y(Y-5)

We move all terms to the left:

-4Y+10-(Y(Y-5))=0


We calculate terms in parentheses: -(Y(Y-5)), so:

Y(Y-5)

We multiply parentheses

Y^2-5Y

Back to the equation:

-(Y^2-5Y)


We get rid of parentheses

-Y^2-4Y+5Y+10=0

We add all the numbers together, and all the variables

-1Y^2+Y+10=0

a = -1; b = 1; c = +10;
Δ = b2-4ac
Δ = 12-4·(-1)·10
Δ = 41
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{-(1)-\sqrt{41}}{2*-1}=\frac{-1-\sqrt{41}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{41}}{2*-1}=\frac{-1+\sqrt{41}}{-2}
$