X^2+18x-29=10

Solution for X^2+18x-29=10 equation:

X^2+18X-29=10

We move all terms to the left:

X^2+18X-29-(10)=0

We add all the numbers together, and all the variables

X^2+18X-39=0

a = 1; b = 18; c = -39;
Δ = b2-4ac
Δ = 182-4·1·(-39)
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-4\sqrt{30}}{2*1}=\frac{-18-4\sqrt{30}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+4\sqrt{30}}{2*1}=\frac{-18+4\sqrt{30}}{2}
$