2X+1/2y=13

Solution for 2X+1/2y=13 equation:

2X+1/2X=13

We move all terms to the left:

2X+1/2X-(13)=0


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We multiply all the terms by the denominator


2X*2X-13*2X+1=0

Wy multiply elements

4X^2-26X+1=0

a = 4; b = -26; c = +1;
Δ = b2-4ac
Δ = -262-4·4·1
Δ = 660
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:

$\sqrt{\Delta}=\sqrt{660}=\sqrt{4*165}=\sqrt{4}*\sqrt{165}=2\sqrt{165}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{165}}{2*4}=\frac{26-2\sqrt{165}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{165}}{2*4}=\frac{26+2\sqrt{165}}{8}
$