4-x^2=1-x

Solution for 4-x^2=1-x equation:

4-x^2=1-x

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1x^2+x+3=0

a = -1; b = 1; c = +3;
Δ = b2-4ac
Δ = 12-4·(-1)·3
Δ = 13
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{-(1)-\sqrt{13}}{2*-1}=\frac{-1-\sqrt{13}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{13}}{2*-1}=\frac{-1+\sqrt{13}}{-2}
$