X2+5x-19x=24

Solution for X2+5x-19x=24 equation:

X2+5X-19X=24

We move all terms to the left:

X2+5X-19X-(24)=0

We add all the numbers together, and all the variables

X^2-14X-24=0

a = 1; b = -14; c = -24;
Δ = b2-4ac
Δ = -142-4·1·(-24)
Δ = 292
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:

$\sqrt{\Delta}=\sqrt{292}=\sqrt{4*73}=\sqrt{4}*\sqrt{73}=2\sqrt{73}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{73}}{2*1}=\frac{14-2\sqrt{73}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{73}}{2*1}=\frac{14+2\sqrt{73}}{2}
$