X^2-14x-69=9

Solution for X^2-14x-69=9 equation:

X^2-14X-69=9

We move all terms to the left:

X^2-14X-69-(9)=0

We add all the numbers together, and all the variables

X^2-14X-78=0

a = 1; b = -14; c = -78;
Δ = b2-4ac
Δ = -142-4·1·(-78)
Δ = 508
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:

$\sqrt{\Delta}=\sqrt{508}=\sqrt{4*127}=\sqrt{4}*\sqrt{127}=2\sqrt{127}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{127}}{2*1}=\frac{14-2\sqrt{127}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{127}}{2*1}=\frac{14+2\sqrt{127}}{2}
$