5/6y+1=-1/5y+9

Solution for 5/6y+1=-1/5y+9 equation:

5/6y+1=-1/5y+9

We move all terms to the left:

5/6y+1-(-1/5y+9)=0


Domain of the equation: 6y!=0

y!=0/6

y!=0

y∈R



Domain of the equation: 5y+9)!=0

y∈R


We get rid of parentheses

5/6y+1/5y-9+1=0

We calculate fractions


25y/30y^2+6y/30y^2-9+1=0

We add all the numbers together, and all the variables

25y/30y^2+6y/30y^2-8=0

We multiply all the terms by the denominator


25y+6y-8*30y^2=0

We add all the numbers together, and all the variables

31y-8*30y^2=0

Wy multiply elements

-240y^2+31y=0

a = -240; b = 31; c = 0;
Δ = b2-4ac
Δ = 312-4·(-240)·0
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-31}{2*-240}=\frac{-62}{-480}
=31/240
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+31}{2*-240}=\frac{0}{-480}
=0
$