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17.7=0.013x^2-1.19x+28.34
We move all terms to the left:
17.7-(0.013x^2-1.19x+28.34)=0
We get rid of parentheses
-0.013x^2+1.19x-28.34+17.7=0
We add all the numbers together, and all the variables
-0.013x^2+1.19x-10.64=0
a = -0.013; b = 1.19; c = -10.64;
Δ = b2-4ac
Δ = 1.192-4·(-0.013)·(-10.64)
Δ = 0.86282
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{-(1.19)-\sqrt{0.86282}}{2*-0.013}=\frac{-1.19-\sqrt{0.86282}}{-0.026} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1.19)+\sqrt{0.86282}}{2*-0.013}=\frac{-1.19+\sqrt{0.86282}}{-0.026} $
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