X^2+4x-127=0

Solution for X^2+4x-127=0 equation:

X^2+4X-127=0

a = 1; b = 4; c = -127;
Δ = b2-4ac
Δ = 42-4·1·(-127)
Δ = 524
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:

$\sqrt{\Delta}=\sqrt{524}=\sqrt{4*131}=\sqrt{4}*\sqrt{131}=2\sqrt{131}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{131}}{2*1}=\frac{-4-2\sqrt{131}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{131}}{2*1}=\frac{-4+2\sqrt{131}}{2}
$