X2-14x-74=2

Solution for X2-14x-74=2 equation:

X2-14X-74=2

We move all terms to the left:

X2-14X-74-(2)=0

We add all the numbers together, and all the variables

X^2-14X-76=0

a = 1; b = -14; c = -76;
Δ = b2-4ac
Δ = -142-4·1·(-76)
Δ = 500
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:

$\sqrt{\Delta}=\sqrt{500}=\sqrt{100*5}=\sqrt{100}*\sqrt{5}=10\sqrt{5}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-10\sqrt{5}}{2*1}=\frac{14-10\sqrt{5}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+10\sqrt{5}}{2*1}=\frac{14+10\sqrt{5}}{2}
$