X2-22x+105=0

Solution for X2-22x+105=0 equation:

X2-22X+105=0

We add all the numbers together, and all the variables

X^2-22X+105=0

a = 1; b = -22; c = +105;
Δ = b2-4ac
Δ = -222-4·1·105
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-8}{2*1}=\frac{14}{2}
=7
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+8}{2*1}=\frac{30}{2}
=15
$