Y=4x(x-5)

Solution for Y=4x(x-5) equation:

=4Y(Y-5)

We move all terms to the left:

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


We calculate terms in parentheses: -(4Y(Y-5)), so:

4Y(Y-5)

We multiply parentheses

4Y^2-20Y

Back to the equation:

-(4Y^2-20Y)


We get rid of parentheses

-4Y^2+20Y=0

a = -4; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·(-4)·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*-4}=\frac{-40}{-8}
=+5
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*-4}=\frac{0}{-8}
=0
$