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1=314.019418x+24673.20799626468x^2
We move all terms to the left:
1-(314.019418x+24673.20799626468x^2)=0
We get rid of parentheses
-24673.20799626468x^2-314.019418x+1=0
We add all the numbers together, and all the variables
-24673.2079963x^2-314.019418x+1=0
a = -24673.2079963; b = -314.019418; c = +1;
Δ = b2-4ac
Δ = -314.0194182-4·(-24673.2079963)·1
Δ = 197301.026866
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{-(-314.019418)-\sqrt{197301.026866}}{2*-24673.2079963}=\frac{314.019418-\sqrt{197301.026866}}{-49346.4159926} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-314.019418)+\sqrt{197301.026866}}{2*-24673.2079963}=\frac{314.019418+\sqrt{197301.026866}}{-49346.4159926} $
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