Y=5x(2x+1)

Solution for Y=5x(2x+1) equation:

=5Y(2Y+1)

We move all terms to the left:

-(5Y(2Y+1))=0


We calculate terms in parentheses: -(5Y(2Y+1)), so:

5Y(2Y+1)

We multiply parentheses

10Y^2+5Y

Back to the equation:

-(10Y^2+5Y)


We get rid of parentheses

-10Y^2-5Y=0

a = -10; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·(-10)·0
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{-(-5)-5}{2*-10}=\frac{0}{-20}
=0
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*-10}=\frac{10}{-20}
=-1/2
$