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6.09x^2+4.57x=8.86
We move all terms to the left:
6.09x^2+4.57x-(8.86)=0
We add all the numbers together, and all the variables
6.09x^2+4.57x-8.86=0
a = 6.09; b = 4.57; c = -8.86;
Δ = b2-4ac
Δ = 4.572-4·6.09·(-8.86)
Δ = 236.7145
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{-(4.57)-\sqrt{236.7145}}{2*6.09}=\frac{-4.57-\sqrt{236.7145}}{12.18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4.57)+\sqrt{236.7145}}{2*6.09}=\frac{-4.57+\sqrt{236.7145}}{12.18} $
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