(4*5y-8y)/5y+7y=0

Solution for (4*5y-8y)/5y+7y=0 equation:

(4*5y-8y)/5y+7y=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R


We add all the numbers together, and all the variables

(-8y+4*5y)/5y+7y=0

We add all the numbers together, and all the variables

7y+(-8y+4*5y)/5y=0

We multiply all the terms by the denominator


7y*5y+(-8y+4*5y)=0

Wy multiply elements

35y^2+(-8y+4*5y)=0

We get rid of parentheses

35y^2-8y+4*5y=0

Wy multiply elements

35y^2-8y+20y=0

We add all the numbers together, and all the variables

35y^2+12y=0

a = 35; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·35·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12}{2*35}=\frac{-24}{70}
=-12/35
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*35}=\frac{0}{70}
=0
$