X2+5x-19.x=-4

Solution for X2+5x-19.x=-4 equation:

X2+5X-19.X=-4

We move all terms to the left:

X2+5X-19.X-(-4)=0

We add all the numbers together, and all the variables

X^2-14X+4=0

a = 1; b = -14; c = +4;
Δ = b2-4ac
Δ = -142-4·1·4
Δ = 180
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-6\sqrt{5}}{2*1}=\frac{14-6\sqrt{5}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+6\sqrt{5}}{2*1}=\frac{14+6\sqrt{5}}{2}
$