X/2+y2=52

Solution for X/2+y2=52 equation:

X/2+X2=52

We move all terms to the left:

X/2+X2-(52)=0

We add all the numbers together, and all the variables

X^2+X/2-52=0

We multiply all the terms by the denominator


X^2*2+X-52*2=0

We add all the numbers together, and all the variables

X^2*2+X-104=0

Wy multiply elements

2X^2+X-104=0

a = 2; b = 1; c = -104;
Δ = b2-4ac
Δ = 12-4·2·(-104)
Δ = 833
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:

$\sqrt{\Delta}=\sqrt{833}=\sqrt{49*17}=\sqrt{49}*\sqrt{17}=7\sqrt{17}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-7\sqrt{17}}{2*2}=\frac{-1-7\sqrt{17}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+7\sqrt{17}}{2*2}=\frac{-1+7\sqrt{17}}{4}
$