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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:We get rid of parentheses
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)
-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} $
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