x^2+6x-47=20

Solution for x^2+6x-47=20 equation:

x^2+6x-47=20

We move all terms to the left:

x^2+6x-47-(20)=0

We add all the numbers together, and all the variables

x^2+6x-67=0

a = 1; b = 6; c = -67;
Δ = b2-4ac
Δ = 62-4·1·(-67)
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-4\sqrt{19}}{2*1}=\frac{-6-4\sqrt{19}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+4\sqrt{19}}{2*1}=\frac{-6+4\sqrt{19}}{2}
$