x2+19x+78=0

Solution for x2+19x+78=0 equation:

x2+19x+78=0

We add all the numbers together, and all the variables

x^2+19x+78=0

a = 1; b = 19; c = +78;
Δ = b2-4ac
Δ = 192-4·1·78
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-7}{2*1}=\frac{-26}{2}
=-13
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+7}{2*1}=\frac{-12}{2}
=-6
$