y+100=10/9y+900

Solution for y+100=10/9y+900 equation:

y+100=10/9y+900

We move all terms to the left:

y+100-(10/9y+900)=0


Domain of the equation: 9y+900)!=0

y∈R


We get rid of parentheses

y-10/9y-900+100=0

We multiply all the terms by the denominator


y*9y-900*9y+100*9y-10=0

Wy multiply elements

9y^2-8100y+900y-10=0

We add all the numbers together, and all the variables

9y^2-7200y-10=0

a = 9; b = -7200; c = -10;
Δ = b2-4ac
Δ = -72002-4·9·(-10)
Δ = 51840360
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:

$\sqrt{\Delta}=\sqrt{51840360}=\sqrt{36*1440010}=\sqrt{36}*\sqrt{1440010}=6\sqrt{1440010}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7200)-6\sqrt{1440010}}{2*9}=\frac{7200-6\sqrt{1440010}}{18}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7200)+6\sqrt{1440010}}{2*9}=\frac{7200+6\sqrt{1440010}}{18}
$