x-1=x^2-49

Solution for x-1=x^2-49 equation:

x-1=x^2-49

We move all terms to the left:

x-1-(x^2-49)=0

We get rid of parentheses

-x^2+x+49-1=0

We add all the numbers together, and all the variables

-1x^2+x+48=0

a = -1; b = 1; c = +48;
Δ = b2-4ac
Δ = 12-4·(-1)·48
Δ = 193
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{-(1)-\sqrt{193}}{2*-1}=\frac{-1-\sqrt{193}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{193}}{2*-1}=\frac{-1+\sqrt{193}}{-2}
$