X^2+6x-19=30

Solution for X^2+6x-19=30 equation:

X^2+6X-19=30

We move all terms to the left:

X^2+6X-19-(30)=0

We add all the numbers together, and all the variables

X^2+6X-49=0

a = 1; b = 6; c = -49;
Δ = b2-4ac
Δ = 62-4·1·(-49)
Δ = 232
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:

$\sqrt{\Delta}=\sqrt{232}=\sqrt{4*58}=\sqrt{4}*\sqrt{58}=2\sqrt{58}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{58}}{2*1}=\frac{-6-2\sqrt{58}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{58}}{2*1}=\frac{-6+2\sqrt{58}}{2}
$