Y=10x/2-x^2

Solution for Y=10x/2-x^2 equation:

=10Y/2-Y^2

We move all terms to the left:

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


Domain of the equation: 2-Y^2)!=0

We move all terms containing Y to the left, all other terms to the right

-Y^2)!=-2

Y!=-2/1

Y!=-2

Y∈R


We get rid of parentheses

Y^2-10Y/2=0

We multiply all the terms by the denominator


Y^2*2-10Y=0

Wy multiply elements

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
$