5y+2=1/210y+4

Solution for 5y+2=1/210y+4 equation:

5y+2=1/210y+4

We move all terms to the left:

5y+2-(1/210y+4)=0


Domain of the equation: 210y+4)!=0

y∈R


We get rid of parentheses

5y-1/210y-4+2=0

We multiply all the terms by the denominator


5y*210y-4*210y+2*210y-1=0

Wy multiply elements

1050y^2-840y+420y-1=0

We add all the numbers together, and all the variables

1050y^2-420y-1=0

a = 1050; b = -420; c = -1;
Δ = b2-4ac
Δ = -4202-4·1050·(-1)
Δ = 180600
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:

$\sqrt{\Delta}=\sqrt{180600}=\sqrt{100*1806}=\sqrt{100}*\sqrt{1806}=10\sqrt{1806}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-420)-10\sqrt{1806}}{2*1050}=\frac{420-10\sqrt{1806}}{2100}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-420)+10\sqrt{1806}}{2*1050}=\frac{420+10\sqrt{1806}}{2100}
$