300+y-450=2/5y

Solution for 300+y-450=2/5y equation:

300+y-450=2/5y

We move all terms to the left:

300+y-450-(2/5y)=0


Domain of the equation: 5y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

y-(+2/5y)+300-450=0

We add all the numbers together, and all the variables

y-(+2/5y)-150=0

We get rid of parentheses

y-2/5y-150=0

We multiply all the terms by the denominator


y*5y-150*5y-2=0

Wy multiply elements

5y^2-750y-2=0

a = 5; b = -750; c = -2;
Δ = b2-4ac
Δ = -7502-4·5·(-2)
Δ = 562540
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:

$\sqrt{\Delta}=\sqrt{562540}=\sqrt{4*140635}=\sqrt{4}*\sqrt{140635}=2\sqrt{140635}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-750)-2\sqrt{140635}}{2*5}=\frac{750-2\sqrt{140635}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-750)+2\sqrt{140635}}{2*5}=\frac{750+2\sqrt{140635}}{10}
$