X+1/2y=60

Solution for X+1/2y=60 equation:

X+1/2X=60

We move all terms to the left:

X+1/2X-(60)=0


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We multiply all the terms by the denominator


X*2X-60*2X+1=0

Wy multiply elements

2X^2-120X+1=0

a = 2; b = -120; c = +1;
Δ = b2-4ac
Δ = -1202-4·2·1
Δ = 14392
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:

$\sqrt{\Delta}=\sqrt{14392}=\sqrt{4*3598}=\sqrt{4}*\sqrt{3598}=2\sqrt{3598}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-2\sqrt{3598}}{2*2}=\frac{120-2\sqrt{3598}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+2\sqrt{3598}}{2*2}=\frac{120+2\sqrt{3598}}{4}
$