0.25(10000)-0.4y=0.06y(y+10000)

Solution for 0.25(10000)-0.4y=0.06y(y+10000) equation:

0.25(10000)-0.4y=0.06y(y+10000)

We move all terms to the left:

0.25(10000)-0.4y-(0.06y(y+10000))=0

We add all the numbers together, and all the variables

-0.4y-(0.06y(y+10000))+0.251=0


We calculate terms in parentheses: -(0.06y(y+10000)), so:

0.06y(y+10000)

We multiply parentheses

0y^2+0y

We add all the numbers together, and all the variables

y^2+y

Back to the equation:

-(y^2+y)


We get rid of parentheses

-y^2-0.4y-y+0.251=0

We add all the numbers together, and all the variables

-1y^2-1.4y+0.251=0

a = -1; b = -1.4; c = +0.251;
Δ = b2-4ac
Δ = -1.42-4·(-1)·0.251
Δ = 2.964
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1.4)-\sqrt{2.964}}{2*-1}=\frac{1.4-\sqrt{2.964}}{-2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1.4)+\sqrt{2.964}}{2*-1}=\frac{1.4+\sqrt{2.964}}{-2}
$