20-x=35-x2

Solution for 20-x=35-x2 equation:

20-x=35-x2

We move all terms to the left:

20-x-(35-x2)=0

We add all the numbers together, and all the variables

-(-1x^2+35)-x+20=0

We add all the numbers together, and all the variables

-(-1x^2+35)-1x+20=0

We get rid of parentheses

1x^2-1x-35+20=0

We add all the numbers together, and all the variables

x^2-1x-15=0

a = 1; b = -1; c = -15;
Δ = b2-4ac
Δ = -12-4·1·(-15)
Δ = 61
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{61}}{2*1}=\frac{1-\sqrt{61}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{61}}{2*1}=\frac{1+\sqrt{61}}{2}
$