86(5x^2)=41

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Solution for 86(5x^2)=41 equation:



86(5x^2)=41
We move all terms to the left:
86(5x^2)-(41)=0
a = 865; b = 0; c = -41;
Δ = b2-4ac
Δ = 02-4·865·(-41)
Δ = 141860
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{141860}=\sqrt{4*35465}=\sqrt{4}*\sqrt{35465}=2\sqrt{35465}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{35465}}{2*865}=\frac{0-2\sqrt{35465}}{1730} =-\frac{2\sqrt{35465}}{1730} =-\frac{\sqrt{35465}}{865} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{35465}}{2*865}=\frac{0+2\sqrt{35465}}{1730} =\frac{2\sqrt{35465}}{1730} =\frac{\sqrt{35465}}{865} $

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