1/2y+X=9

Solution for 1/2y+X=9 equation:

1/2y+y=9

We move all terms to the left:

1/2y+y-(9)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We add all the numbers together, and all the variables

y+1/2y-9=0

We multiply all the terms by the denominator


y*2y-9*2y+1=0

Wy multiply elements

2y^2-18y+1=0

a = 2; b = -18; c = +1;
Δ = b2-4ac
Δ = -182-4·2·1
Δ = 316
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:

$\sqrt{\Delta}=\sqrt{316}=\sqrt{4*79}=\sqrt{4}*\sqrt{79}=2\sqrt{79}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{79}}{2*2}=\frac{18-2\sqrt{79}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{79}}{2*2}=\frac{18+2\sqrt{79}}{4}
$