4x-4=x^2-49

Solution for 4x-4=x^2-49 equation:

4x-4=x^2-49

We move all terms to the left:

4x-4-(x^2-49)=0

We get rid of parentheses

-x^2+4x+49-4=0

We add all the numbers together, and all the variables

-1x^2+4x+45=0

a = -1; b = 4; c = +45;
Δ = b2-4ac
Δ = 42-4·(-1)·45
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-14}{2*-1}=\frac{-18}{-2}
=+9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+14}{2*-1}=\frac{10}{-2}
=-5
$