x2Y-2Y=42,X+2=5

Solution for x2Y-2Y=42,X+2=5 equation:

x2-2=42.x+2=5

We move all terms to the left:

x2-2-(42.x+2)=0

We add all the numbers together, and all the variables

x^2-(42.x+2)-2=0

We get rid of parentheses

x^2-42.x-2-2=0

We add all the numbers together, and all the variables

x^2-42x-4=0

a = 1; b = -42; c = -4;
Δ = b2-4ac
Δ = -422-4·1·(-4)
Δ = 1780
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:

$\sqrt{\Delta}=\sqrt{1780}=\sqrt{4*445}=\sqrt{4}*\sqrt{445}=2\sqrt{445}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{445}}{2*1}=\frac{42-2\sqrt{445}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{445}}{2*1}=\frac{42+2\sqrt{445}}{2}
$