x^2+4x-137=0

Solution for x^2+4x-137=0 equation:

x^2+4x-137=0

a = 1; b = 4; c = -137;
Δ = b2-4ac
Δ = 42-4·1·(-137)
Δ = 564
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:

$\sqrt{\Delta}=\sqrt{564}=\sqrt{4*141}=\sqrt{4}*\sqrt{141}=2\sqrt{141}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{141}}{2*1}=\frac{-4-2\sqrt{141}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{141}}{2*1}=\frac{-4+2\sqrt{141}}{2}
$