x^2+14x-69=30

Solution for x^2+14x-69=30 equation:

x^2+14x-69=30

We move all terms to the left:

x^2+14x-69-(30)=0

We add all the numbers together, and all the variables

x^2+14x-99=0

a = 1; b = 14; c = -99;
Δ = b2-4ac
Δ = 142-4·1·(-99)
Δ = 592
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:

$\sqrt{\Delta}=\sqrt{592}=\sqrt{16*37}=\sqrt{16}*\sqrt{37}=4\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-4\sqrt{37}}{2*1}=\frac{-14-4\sqrt{37}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+4\sqrt{37}}{2*1}=\frac{-14+4\sqrt{37}}{2}
$