49-y=7/36y

Solution for 49-y=7/36y equation:

49-y=7/36y

We move all terms to the left:

49-y-(7/36y)=0


Domain of the equation: 36y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

-y-(+7/36y)+49=0

We add all the numbers together, and all the variables

-1y-(+7/36y)+49=0

We get rid of parentheses

-1y-7/36y+49=0

We multiply all the terms by the denominator


-1y*36y+49*36y-7=0

Wy multiply elements

-36y^2+1764y-7=0

a = -36; b = 1764; c = -7;
Δ = b2-4ac
Δ = 17642-4·(-36)·(-7)
Δ = 3110688
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:

$\sqrt{\Delta}=\sqrt{3110688}=\sqrt{144*21602}=\sqrt{144}*\sqrt{21602}=12\sqrt{21602}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1764)-12\sqrt{21602}}{2*-36}=\frac{-1764-12\sqrt{21602}}{-72}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1764)+12\sqrt{21602}}{2*-36}=\frac{-1764+12\sqrt{21602}}{-72}
$