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0.02x+0.01x(6000-x)=97
We move all terms to the left:
0.02x+0.01x(6000-x)-(97)=0
We add all the numbers together, and all the variables
0.02x+0.01x(-1x+6000)-97=0
We multiply parentheses
0x^2+0.02x+0x-97=0
We add all the numbers together, and all the variables
x^2+1.02x-97=0
a = 1; b = 1.02; c = -97;
Δ = b2-4ac
Δ = 1.022-4·1·(-97)
Δ = 389.0404
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{-(1.02)-\sqrt{389.0404}}{2*1}=\frac{-1.02-\sqrt{389.0404}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1.02)+\sqrt{389.0404}}{2*1}=\frac{-1.02+\sqrt{389.0404}}{2} $
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