-x+1=-x2+4x-3

Solution for -x+1=-x2+4x-3 equation:

-x+1=-x2+4x-3

We move all terms to the left:

-x+1-(-x2+4x-3)=0

We add all the numbers together, and all the variables

-(-1x^2+4x-3)-x+1=0

We add all the numbers together, and all the variables

-(-1x^2+4x-3)-1x+1=0

We get rid of parentheses

1x^2-4x-1x+3+1=0

We add all the numbers together, and all the variables

x^2-5x+4=0

a = 1; b = -5; c = +4;
Δ = b2-4ac
Δ = -52-4·1·4
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-3}{2*1}=\frac{2}{2}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+3}{2*1}=\frac{8}{2}
=4
$