x2+19x-84=0

Solution for x2+19x-84=0 equation:

x2+19x-84=0

We add all the numbers together, and all the variables

x^2+19x-84=0

a = 1; b = 19; c = -84;
Δ = b2-4ac
Δ = 192-4·1·(-84)
Δ = 697
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-\sqrt{697}}{2*1}=\frac{-19-\sqrt{697}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+\sqrt{697}}{2*1}=\frac{-19+\sqrt{697}}{2}
$