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3.0908x^2+17.685x+1.2414=89
We move all terms to the left:
3.0908x^2+17.685x+1.2414-(89)=0
We add all the numbers together, and all the variables
3.0908x^2+17.685x-87.7586=0
a = 3.0908; b = 17.685; c = -87.7586;
Δ = b2-4ac
Δ = 17.6852-4·3.0908·(-87.7586)
Δ = 1397.73634852
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{-(17.685)-\sqrt{1397.73634852}}{2*3.0908}=\frac{-17.685-\sqrt{1397.73634852}}{6.1816} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17.685)+\sqrt{1397.73634852}}{2*3.0908}=\frac{-17.685+\sqrt{1397.73634852}}{6.1816} $
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