10/2y+15(-2y+3y)=220y

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Solution for 10/2y+15(-2y+3y)=220y equation:



10/2y+15(-2y+3y)=220y
We move all terms to the left:
10/2y+15(-2y+3y)-(220y)=0
Domain of the equation: 2y!=0
y!=0/2
y!=0
y∈R
We add all the numbers together, and all the variables
10/2y+15(+y)-220y=0
We add all the numbers together, and all the variables
-220y+10/2y+15(+y)=0
We multiply parentheses
-220y+10/2y+15y=0
We multiply all the terms by the denominator
-220y*2y+15y*2y+10=0
Wy multiply elements
-440y^2+30y^2+10=0
We add all the numbers together, and all the variables
-410y^2+10=0
a = -410; b = 0; c = +10;
Δ = b2-4ac
Δ = 02-4·(-410)·10
Δ = 16400
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:
$\sqrt{\Delta}=\sqrt{16400}=\sqrt{400*41}=\sqrt{400}*\sqrt{41}=20\sqrt{41}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{41}}{2*-410}=\frac{0-20\sqrt{41}}{-820} =-\frac{20\sqrt{41}}{-820} =-\frac{\sqrt{41}}{-41} $
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{41}}{2*-410}=\frac{0+20\sqrt{41}}{-820} =\frac{20\sqrt{41}}{-820} =\frac{\sqrt{41}}{-41} $

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