x^2+138x-4761=0

Solution for x^2+138x-4761=0 equation:

x^2+138x-4761=0

a = 1; b = 138; c = -4761;
Δ = b2-4ac
Δ = 1382-4·1·(-4761)
Δ = 38088
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:

$\sqrt{\Delta}=\sqrt{38088}=\sqrt{19044*2}=\sqrt{19044}*\sqrt{2}=138\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(138)-138\sqrt{2}}{2*1}=\frac{-138-138\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(138)+138\sqrt{2}}{2*1}=\frac{-138+138\sqrt{2}}{2}
$