1/2y+2=5y=

Solution for 1/2y+2=5y= equation:

1/2y+2=5y=

We move all terms to the left:

1/2y+2-(5y)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We add all the numbers together, and all the variables

-5y+1/2y+2=0

We multiply all the terms by the denominator


-5y*2y+2*2y+1=0

Wy multiply elements

-10y^2+4y+1=0

a = -10; b = 4; c = +1;
Δ = b2-4ac
Δ = 42-4·(-10)·1
Δ = 56
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:

$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{14}}{2*-10}=\frac{-4-2\sqrt{14}}{-20}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{14}}{2*-10}=\frac{-4+2\sqrt{14}}{-20}
$