x2+22x+57=0.

Solution for x2+22x+57=0. equation:

x2+22x+57=0.

We add all the numbers together, and all the variables

x^2+22x+57=0

a = 1; b = 22; c = +57;
Δ = b2-4ac
Δ = 222-4·1·57
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-16}{2*1}=\frac{-38}{2}
=-19
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+16}{2*1}=\frac{-6}{2}
=-3
$