x^2-7x-31=49

Solution for x^2-7x-31=49 equation:

x^2-7x-31=49

We move all terms to the left:

x^2-7x-31-(49)=0

We add all the numbers together, and all the variables

x^2-7x-80=0

a = 1; b = -7; c = -80;
Δ = b2-4ac
Δ = -72-4·1·(-80)
Δ = 369
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:

$\sqrt{\Delta}=\sqrt{369}=\sqrt{9*41}=\sqrt{9}*\sqrt{41}=3\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-3\sqrt{41}}{2*1}=\frac{7-3\sqrt{41}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+3\sqrt{41}}{2*1}=\frac{7+3\sqrt{41}}{2}
$