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

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

=2Y(2Y+5)+2(2Y+5)(Y+3)+2(Y)(Y+3)

We move all terms to the left:

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

We multiply parentheses ..

-(2Y(2Y+5)+2(+2Y^2+6Y+5Y+15)+2Y(Y+3))=0


We calculate terms in parentheses: -(2Y(2Y+5)+2(+2Y^2+6Y+5Y+15)+2Y(Y+3)), so:

2Y(2Y+5)+2(+2Y^2+6Y+5Y+15)+2Y(Y+3)

determiningTheFunctionDomain
2(+2Y^2+6Y+5Y+15)+2Y(2Y+5)+2Y(Y+3)

We multiply parentheses

4Y^2+4Y^2+2Y^2+12Y+10Y+10Y+6Y+30

We add all the numbers together, and all the variables

10Y^2+38Y+30

Back to the equation:

-(10Y^2+38Y+30)


We get rid of parentheses

-10Y^2-38Y-30=0

a = -10; b = -38; c = -30;
Δ = b2-4ac
Δ = -382-4·(-10)·(-30)
Δ = 244
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-2\sqrt{61}}{2*-10}=\frac{38-2\sqrt{61}}{-20}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+2\sqrt{61}}{2*-10}=\frac{38+2\sqrt{61}}{-20}
$