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4x=-0.02x^2+800x-4000
We move all terms to the left:
4x-(-0.02x^2+800x-4000)=0
We get rid of parentheses
0.02x^2-800x+4x+4000=0
We add all the numbers together, and all the variables
0.02x^2-796x+4000=0
a = 0.02; b = -796; c = +4000;
Δ = b2-4ac
Δ = -7962-4·0.02·4000
Δ = 633296
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{633296}=\sqrt{16*39581}=\sqrt{16}*\sqrt{39581}=4\sqrt{39581}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-796)-4\sqrt{39581}}{2*0.02}=\frac{796-4\sqrt{39581}}{0.04} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-796)+4\sqrt{39581}}{2*0.02}=\frac{796+4\sqrt{39581}}{0.04} $
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