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0.9x^2-0.6x-0.009=-0.08
We move all terms to the left:
0.9x^2-0.6x-0.009-(-0.08)=0
We add all the numbers together, and all the variables
0.9x^2-0.6x+0.071=0
a = 0.9; b = -0.6; c = +0.071;
Δ = b2-4ac
Δ = -0.62-4·0.9·0.071
Δ = 0.1044
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{-(-0.6)-\sqrt{0.1044}}{2*0.9}=\frac{0.6-\sqrt{0.1044}}{1.8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.6)+\sqrt{0.1044}}{2*0.9}=\frac{0.6+\sqrt{0.1044}}{1.8} $
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