x^2+6x-138=0

Solution for x^2+6x-138=0 equation:

x^2+6x-138=0

a = 1; b = 6; c = -138;
Δ = b2-4ac
Δ = 62-4·1·(-138)
Δ = 588
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:

$\sqrt{\Delta}=\sqrt{588}=\sqrt{196*3}=\sqrt{196}*\sqrt{3}=14\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-14\sqrt{3}}{2*1}=\frac{-6-14\sqrt{3}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+14\sqrt{3}}{2*1}=\frac{-6+14\sqrt{3}}{2}
$