7/2y+y=4500

Solution for 7/2y+y=4500 equation:

7/2y+y=4500

We move all terms to the left:

7/2y+y-(4500)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We add all the numbers together, and all the variables

y+7/2y-4500=0

We multiply all the terms by the denominator


y*2y-4500*2y+7=0

Wy multiply elements

2y^2-9000y+7=0

a = 2; b = -9000; c = +7;
Δ = b2-4ac
Δ = -90002-4·2·7
Δ = 80999944
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:

$\sqrt{\Delta}=\sqrt{80999944}=\sqrt{4*20249986}=\sqrt{4}*\sqrt{20249986}=2\sqrt{20249986}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9000)-2\sqrt{20249986}}{2*2}=\frac{9000-2\sqrt{20249986}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9000)+2\sqrt{20249986}}{2*2}=\frac{9000+2\sqrt{20249986}}{4}
$