x2+y2=34.x-y=2

Solution for x2+y2=34.x-y=2 equation:

X2+X2=34.X-X=2

We move all terms to the left:

X2+X2-(34.X-X)=0

We add all the numbers together, and all the variables

X2+X2-(+33X)=0

We add all the numbers together, and all the variables

2X^2-(+33X)=0

We get rid of parentheses

2X^2-33X=0

a = 2; b = -33; c = 0;
Δ = b2-4ac
Δ = -332-4·2·0
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-33}{2*2}=\frac{0}{4}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+33}{2*2}=\frac{66}{4}
=16+1/2
$