X2+14x-347=0

Solution for X2+14x-347=0 equation:

X2+14X-347=0

We add all the numbers together, and all the variables

X^2+14X-347=0

a = 1; b = 14; c = -347;
Δ = b2-4ac
Δ = 142-4·1·(-347)
Δ = 1584
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:

$\sqrt{\Delta}=\sqrt{1584}=\sqrt{144*11}=\sqrt{144}*\sqrt{11}=12\sqrt{11}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-12\sqrt{11}}{2*1}=\frac{-14-12\sqrt{11}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+12\sqrt{11}}{2*1}=\frac{-14+12\sqrt{11}}{2}
$