X^2+18x+32=3

Solution for X^2+18x+32=3 equation:

X^2+18X+32=3

We move all terms to the left:

X^2+18X+32-(3)=0

We add all the numbers together, and all the variables

X^2+18X+29=0

a = 1; b = 18; c = +29;
Δ = b2-4ac
Δ = 182-4·1·29
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-4\sqrt{13}}{2*1}=\frac{-18-4\sqrt{13}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+4\sqrt{13}}{2*1}=\frac{-18+4\sqrt{13}}{2}
$