x2+6x-0.588=169.412

Solution for x2+6x-0.588=169.412 equation:

x2+6x-0.588=169.412

We move all terms to the left:

x2+6x-0.588-(169.412)=0

We add all the numbers together, and all the variables

x^2+6x-170=0

a = 1; b = 6; c = -170;
Δ = b2-4ac
Δ = 62-4·1·(-170)
Δ = 716
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:

$\sqrt{\Delta}=\sqrt{716}=\sqrt{4*179}=\sqrt{4}*\sqrt{179}=2\sqrt{179}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{179}}{2*1}=\frac{-6-2\sqrt{179}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{179}}{2*1}=\frac{-6+2\sqrt{179}}{2}
$