x2-589x=98.5

Solution for x2-589x=98.5 equation:

x2-589x=98.5

We move all terms to the left:

x2-589x-(98.5)=0

We add all the numbers together, and all the variables

x^2-589x-98.5=0

a = 1; b = -589; c = -98.5;
Δ = b2-4ac
Δ = -5892-4·1·(-98.5)
Δ = 347315
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{-(-589)-\sqrt{347315}}{2*1}=\frac{589-\sqrt{347315}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-589)+\sqrt{347315}}{2*1}=\frac{589+\sqrt{347315}}{2}
$