x2-49;x=-1

Solution for x2-49;x=-1 equation:

x2-49x=-1

We move all terms to the left:

x2-49x-(-1)=0

We add all the numbers together, and all the variables

x^2-49x+1=0

a = 1; b = -49; c = +1;
Δ = b2-4ac
Δ = -492-4·1·1
Δ = 2397
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{-(-49)-\sqrt{2397}}{2*1}=\frac{49-\sqrt{2397}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-49)+\sqrt{2397}}{2*1}=\frac{49+\sqrt{2397}}{2}
$