7x-1=x^2

Solution for 7x-1=x^2 equation:

7x-1=x^2

We move all terms to the left:

7x-1-(x^2)=0

determiningTheFunctionDomain
-x^2+7x-1=0

We add all the numbers together, and all the variables

-1x^2+7x-1=0

a = -1; b = 7; c = -1;
Δ = b2-4ac
Δ = 72-4·(-1)·(-1)
Δ = 45
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:

$\sqrt{\Delta}=\sqrt{45}=\sqrt{9*5}=\sqrt{9}*\sqrt{5}=3\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-3\sqrt{5}}{2*-1}=\frac{-7-3\sqrt{5}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+3\sqrt{5}}{2*-1}=\frac{-7+3\sqrt{5}}{-2}
$