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x^2=17.1136-8.404x+0.995x^2
We move all terms to the left:
x^2-(17.1136-8.404x+0.995x^2)=0
We get rid of parentheses
x^2-0.995x^2+8.404x-17.1136=0
We add all the numbers together, and all the variables
0.005x^2+8.404x-17.1136=0
a = 0.005; b = 8.404; c = -17.1136;
Δ = b2-4ac
Δ = 8.4042-4·0.005·(-17.1136)
Δ = 70.969488
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{-(8.404)-\sqrt{70.969488}}{2*0.005}=\frac{-8.404-\sqrt{70.969488}}{0.01} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8.404)+\sqrt{70.969488}}{2*0.005}=\frac{-8.404+\sqrt{70.969488}}{0.01} $
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