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0.12x+0.08x(10.000-x)=1000
We move all terms to the left:
0.12x+0.08x(10.000-x)-(1000)=0
We add all the numbers together, and all the variables
0.12x+0.08x(-1x+10)-1000=0
We multiply parentheses
0x^2+0.12x+0x-1000=0
We add all the numbers together, and all the variables
x^2+1.12x-1000=0
a = 1; b = 1.12; c = -1000;
Δ = b2-4ac
Δ = 1.122-4·1·(-1000)
Δ = 4001.2544
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1.12)-\sqrt{4001.2544}}{2*1}=\frac{-1.12-\sqrt{4001.2544}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1.12)+\sqrt{4001.2544}}{2*1}=\frac{-1.12+\sqrt{4001.2544}}{2} $
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