X2-14x-12=0

Solution for X2-14x-12=0 equation:

X2-14X-12=0

We add all the numbers together, and all the variables

X^2-14X-12=0

a = 1; b = -14; c = -12;
Δ = b2-4ac
Δ = -142-4·1·(-12)
Δ = 244
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:

$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{61}}{2*1}=\frac{14-2\sqrt{61}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{61}}{2*1}=\frac{14+2\sqrt{61}}{2}
$