x^2+x/86.6-259=0

Solution for x^2+x/86.6-259=0 equation:

x^2+x/86.6-259=0

We multiply all the terms by the denominator


x^2*86.6+x-259*86.6=0

We add all the numbers together, and all the variables

x^2*86.6+x-22429.4=0

Wy multiply elements

86.6x^2+x-22429.4=0

a = 86.6; b = 1; c = -22429.4;
Δ = b2-4ac
Δ = 12-4·86.6·(-22429.4)
Δ = 7769545.16
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{-(1)-\sqrt{7769545.16}}{2*86.6}=\frac{-1-\sqrt{7769545.16}}{173.2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{7769545.16}}{2*86.6}=\frac{-1+\sqrt{7769545.16}}{173.2}
$