Y=x(2x+10)

Solution for Y=x(2x+10) equation:

=Y(2Y+10)

We move all terms to the left:

-(Y(2Y+10))=0


We calculate terms in parentheses: -(Y(2Y+10)), so:

Y(2Y+10)

We multiply parentheses

2Y^2+10Y

Back to the equation:

-(2Y^2+10Y)


We get rid of parentheses

-2Y^2-10Y=0

a = -2; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·(-2)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*-2}=\frac{0}{-4}
=0
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*-2}=\frac{20}{-4}
=-5
$