Y=30x-10x2

Solution for Y=30x-10x2 equation:

=30Y-10Y^2

We move all terms to the left:

-(30Y-10Y^2)=0

We get rid of parentheses

10Y^2-30Y=0

a = 10; b = -30; c = 0;
Δ = b2-4ac
Δ = -302-4·10·0
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-30}{2*10}=\frac{0}{20}
=0
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+30}{2*10}=\frac{60}{20}
=3
$