x^2+12x-307=0

Solution for x^2+12x-307=0 equation:

x^2+12x-307=0

a = 1; b = 12; c = -307;
Δ = b2-4ac
Δ = 122-4·1·(-307)
Δ = 1372
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:

$\sqrt{\Delta}=\sqrt{1372}=\sqrt{196*7}=\sqrt{196}*\sqrt{7}=14\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-14\sqrt{7}}{2*1}=\frac{-12-14\sqrt{7}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+14\sqrt{7}}{2*1}=\frac{-12+14\sqrt{7}}{2}
$