(X)=x2-7x+1

Solution for (X)=x2-7x+1 equation:

(X)=X2-7X+1

We move all terms to the left:

(X)-(X2-7X+1)=0

We add all the numbers together, and all the variables

-(+X^2-7X+1)+X=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1X^2+8X-1=0

a = -1; b = 8; c = -1;
Δ = b2-4ac
Δ = 82-4·(-1)·(-1)
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{15}}{2*-1}=\frac{-8-2\sqrt{15}}{-2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{15}}{2*-1}=\frac{-8+2\sqrt{15}}{-2}
$