1+(5/9)y=(14(54y+108))

Solution for 1+(5/9)y=(14(54y+108)) equation:

1+(5/9)y=(14(54y+108))

We move all terms to the left:

1+(5/9)y-((14(54y+108)))=0


Domain of the equation: 9)y!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

(+5/9)y-((14(54y+108)))+1=0

We multiply parentheses

5y^2-((14(54y+108)))+1=0


We calculate terms in parentheses: -((14(54y+108))), so:

(14(54y+108))


We calculate terms in parentheses: +(14(54y+108)), so:

14(54y+108)

We multiply parentheses

756y+1512

Back to the equation:

+(756y+1512)


We get rid of parentheses

756y+1512

Back to the equation:

-(756y+1512)


We get rid of parentheses

5y^2-756y-1512+1=0

We add all the numbers together, and all the variables

5y^2-756y-1511=0

a = 5; b = -756; c = -1511;
Δ = b2-4ac
Δ = -7562-4·5·(-1511)
Δ = 601756
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:

$\sqrt{\Delta}=\sqrt{601756}=\sqrt{4*150439}=\sqrt{4}*\sqrt{150439}=2\sqrt{150439}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-756)-2\sqrt{150439}}{2*5}=\frac{756-2\sqrt{150439}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-756)+2\sqrt{150439}}{2*5}=\frac{756+2\sqrt{150439}}{10}
$