Y+3/5y+2y=36.

Solution for Y+3/5y+2y=36. equation:

+3/5Y+2Y=36.

We move all terms to the left:

+3/5Y+2Y-(36.)=0


Domain of the equation: 5Y!=0

Y!=0/5

Y!=0

Y∈R


We add all the numbers together, and all the variables

3/5Y+2Y-36=0

We add all the numbers together, and all the variables

2Y+3/5Y-36=0

We multiply all the terms by the denominator


2Y*5Y-36*5Y+3=0

Wy multiply elements

10Y^2-180Y+3=0

a = 10; b = -180; c = +3;
Δ = b2-4ac
Δ = -1802-4·10·3
Δ = 32280
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:

$\sqrt{\Delta}=\sqrt{32280}=\sqrt{4*8070}=\sqrt{4}*\sqrt{8070}=2\sqrt{8070}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-2\sqrt{8070}}{2*10}=\frac{180-2\sqrt{8070}}{20}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+2\sqrt{8070}}{2*10}=\frac{180+2\sqrt{8070}}{20}
$