2y-7=1/5y+2

Solution for 2y-7=1/5y+2 equation:

2y-7=1/5y+2

We move all terms to the left:

2y-7-(1/5y+2)=0


Domain of the equation: 5y+2)!=0

y∈R


We get rid of parentheses

2y-1/5y-2-7=0

We multiply all the terms by the denominator


2y*5y-2*5y-7*5y-1=0

Wy multiply elements

10y^2-10y-35y-1=0

We add all the numbers together, and all the variables

10y^2-45y-1=0

a = 10; b = -45; c = -1;
Δ = b2-4ac
Δ = -452-4·10·(-1)
Δ = 2065
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-\sqrt{2065}}{2*10}=\frac{45-\sqrt{2065}}{20}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{2065}}{2*10}=\frac{45+\sqrt{2065}}{20}
$