X2-4x-9=29

Solution for X2-4x-9=29 equation:

X2-4X-9=29

We move all terms to the left:

X2-4X-9-(29)=0

We add all the numbers together, and all the variables

X^2-4X-38=0

a = 1; b = -4; c = -38;
Δ = b2-4ac
Δ = -42-4·1·(-38)
Δ = 168
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:

$\sqrt{\Delta}=\sqrt{168}=\sqrt{4*42}=\sqrt{4}*\sqrt{42}=2\sqrt{42}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{42}}{2*1}=\frac{4-2\sqrt{42}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{42}}{2*1}=\frac{4+2\sqrt{42}}{2}
$