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126=0.006x^2+0.02x+120
We move all terms to the left:
126-(0.006x^2+0.02x+120)=0
We get rid of parentheses
-0.006x^2-0.02x-120+126=0
We add all the numbers together, and all the variables
-0.006x^2-0.02x+6=0
a = -0.006; b = -0.02; c = +6;
Δ = b2-4ac
Δ = -0.022-4·(-0.006)·6
Δ = 0.1444
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{-(-0.02)-\sqrt{0.1444}}{2*-0.006}=\frac{0.02-\sqrt{0.1444}}{-0.012} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.02)+\sqrt{0.1444}}{2*-0.006}=\frac{0.02+\sqrt{0.1444}}{-0.012} $
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