X^2-14x-9=6

Solution for X^2-14x-9=6 equation:

X^2-14X-9=6

We move all terms to the left:

X^2-14X-9-(6)=0

We add all the numbers together, and all the variables

X^2-14X-15=0

a = 1; b = -14; c = -15;
Δ = b2-4ac
Δ = -142-4·1·(-15)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-16}{2*1}=\frac{-2}{2}
=-1
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+16}{2*1}=\frac{30}{2}
=15
$