X2-18x+42=0

Solution for X2-18x+42=0 equation:

X2-18X+42=0

We add all the numbers together, and all the variables

X^2-18X+42=0

a = 1; b = -18; c = +42;
Δ = b2-4ac
Δ = -182-4·1·42
Δ = 156
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:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{39}}{2*1}=\frac{18-2\sqrt{39}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{39}}{2*1}=\frac{18+2\sqrt{39}}{2}
$