(1/9y+1)+6y=56

Solution for (1/9y+1)+6y=56 equation:

(1/9y+1)+6y=56

We move all terms to the left:

(1/9y+1)+6y-(56)=0


Domain of the equation: 9y+1)!=0

y∈R


We add all the numbers together, and all the variables

6y+(1/9y+1)-56=0

We get rid of parentheses

6y+1/9y+1-56=0

We multiply all the terms by the denominator


6y*9y+1*9y-56*9y+1=0

Wy multiply elements

54y^2+9y-504y+1=0

We add all the numbers together, and all the variables

54y^2-495y+1=0

a = 54; b = -495; c = +1;
Δ = b2-4ac
Δ = -4952-4·54·1
Δ = 244809
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:

$\sqrt{\Delta}=\sqrt{244809}=\sqrt{9*27201}=\sqrt{9}*\sqrt{27201}=3\sqrt{27201}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-495)-3\sqrt{27201}}{2*54}=\frac{495-3\sqrt{27201}}{108}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-495)+3\sqrt{27201}}{2*54}=\frac{495+3\sqrt{27201}}{108}
$