0.06=0.14y(3000-y)+0.42y

Solution for 0.06=0.14y(3000-y)+0.42y equation:

0.06=0.14y(3000-y)+0.42y

We move all terms to the left:

0.06-(0.14y(3000-y)+0.42y)=0

We add all the numbers together, and all the variables

-(0.14y(-1y+3000)+0.42y)+0.06=0


We calculate terms in parentheses: -(0.14y(-1y+3000)+0.42y), so:

0.14y(-1y+3000)+0.42y

We add all the numbers together, and all the variables

0.42y+0.14y(-1y+3000)

We multiply parentheses

0y^2+0.42y+0y

We add all the numbers together, and all the variables

y^2+1.42y

Back to the equation:

-(y^2+1.42y)


We get rid of parentheses

-y^2-1.42y+0.06=0

We add all the numbers together, and all the variables

-1y^2-1.42y+0.06=0

a = -1; b = -1.42; c = +0.06;
Δ = b2-4ac
Δ = -1.422-4·(-1)·0.06
Δ = 2.2564
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{-(-1.42)-\sqrt{2.2564}}{2*-1}=\frac{1.42-\sqrt{2.2564}}{-2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1.42)+\sqrt{2.2564}}{2*-1}=\frac{1.42+\sqrt{2.2564}}{-2}
$