Y=x(3x+15)

Solution for Y=x(3x+15) equation:

=Y(3Y+15)

We move all terms to the left:

-(Y(3Y+15))=0


We calculate terms in parentheses: -(Y(3Y+15)), so:

Y(3Y+15)

We multiply parentheses

3Y^2+15Y

Back to the equation:

-(3Y^2+15Y)


We get rid of parentheses

-3Y^2-15Y=0

a = -3; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·(-3)·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15}{2*-3}=\frac{0}{-6}
=0
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*-3}=\frac{30}{-6}
=-5
$