Y=5(x-2)(x-3)

Solution for Y=5(x-2)(x-3) equation:

=5(Y-2)(Y-3)

We move all terms to the left:

-(5(Y-2)(Y-3))=0

We multiply parentheses ..

-(5(+Y^2-3Y-2Y+6))=0


We calculate terms in parentheses: -(5(+Y^2-3Y-2Y+6)), so:

5(+Y^2-3Y-2Y+6)

We multiply parentheses

5Y^2-15Y-10Y+30

We add all the numbers together, and all the variables

5Y^2-25Y+30

Back to the equation:

-(5Y^2-25Y+30)


We get rid of parentheses

-5Y^2+25Y-30=0

a = -5; b = 25; c = -30;
Δ = b2-4ac
Δ = 252-4·(-5)·(-30)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-5}{2*-5}=\frac{-30}{-10}
=+3
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+5}{2*-5}=\frac{-20}{-10}
=+2
$