y/2+y^2/y+1=6

Solution for y/2+y^2/y+1=6 equation:

y/2+y^2/y+1=6

We move all terms to the left:

y/2+y^2/y+1-(6)=0


Domain of the equation: y!=0

y∈R


We add all the numbers together, and all the variables

y^2/y+y/2-5=0

We calculate fractions


2y^2/2y+y^2/2y-5=0

We multiply all the terms by the denominator


2y^2+y^2-5*2y=0

We add all the numbers together, and all the variables

3y^2-5*2y=0

Wy multiply elements

3y^2-10y=0

a = 3; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·3·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*3}=\frac{0}{6}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*3}=\frac{20}{6}
=3+1/3
$