22.5(10-y)+27/5y=250

Solution for 22.5(10-y)+27/5y=250 equation:

22.5(10-y)+27/5y=250

We move all terms to the left:

22.5(10-y)+27/5y-(250)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R


We add all the numbers together, and all the variables

22.5(-1y+10)+27/5y-250=0

We multiply parentheses

-22.5y+27/5y+225-250=0

We multiply all the terms by the denominator


-(22.5y)*5y+225*5y-250*5y+27=0

We add all the numbers together, and all the variables

-(+22.5y)*5y+225*5y-250*5y+27=0

We multiply parentheses

-110y^2+225*5y-250*5y+27=0

Wy multiply elements

-110y^2+1125y-1250y+27=0

We add all the numbers together, and all the variables

-110y^2-125y+27=0

a = -110; b = -125; c = +27;
Δ = b2-4ac
Δ = -1252-4·(-110)·27
Δ = 27505
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-125)-\sqrt{27505}}{2*-110}=\frac{125-\sqrt{27505}}{-220}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-125)+\sqrt{27505}}{2*-110}=\frac{125+\sqrt{27505}}{-220}
$