x^2-7x+49=121

Solution for x^2-7x+49=121 equation:

x^2-7x+49=121

We move all terms to the left:

x^2-7x+49-(121)=0

We add all the numbers together, and all the variables

x^2-7x-72=0

a = 1; b = -7; c = -72;
Δ = b2-4ac
Δ = -72-4·1·(-72)
Δ = 337
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{337}}{2*1}=\frac{7-\sqrt{337}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{337}}{2*1}=\frac{7+\sqrt{337}}{2}
$