y-1/2y=13

Solution for y-1/2y=13 equation:

y-1/2y=13

We move all terms to the left:

y-1/2y-(13)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We multiply all the terms by the denominator


y*2y-13*2y-1=0

Wy multiply elements

2y^2-26y-1=0

a = 2; b = -26; c = -1;
Δ = b2-4ac
Δ = -262-4·2·(-1)
Δ = 684
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{684}=\sqrt{36*19}=\sqrt{36}*\sqrt{19}=6\sqrt{19}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-6\sqrt{19}}{2*2}=\frac{26-6\sqrt{19}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+6\sqrt{19}}{2*2}=\frac{26+6\sqrt{19}}{4}
$