x2+21x+38=0

Solution for x2+21x+38=0 equation:

x2+21x+38=0

We add all the numbers together, and all the variables

x^2+21x+38=0

a = 1; b = 21; c = +38;
Δ = b2-4ac
Δ = 212-4·1·38
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-17}{2*1}=\frac{-38}{2}
=-19
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+17}{2*1}=\frac{-4}{2}
=-2
$