1/4(y)+5=1/7(y)

Solution for 1/4(y)+5=1/7(y) equation:

1/4(y)+5=1/7(y)

We move all terms to the left:

1/4(y)+5-(1/7(y))=0


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R



Domain of the equation: 7y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

1/4y-(+1/7y)+5=0

We get rid of parentheses

1/4y-1/7y+5=0

We calculate fractions


7y/28y^2+(-4y)/28y^2+5=0

We multiply all the terms by the denominator


7y+(-4y)+5*28y^2=0

Wy multiply elements

140y^2+7y+(-4y)=0

We get rid of parentheses

140y^2+7y-4y=0

We add all the numbers together, and all the variables

140y^2+3y=0

a = 140; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·140·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*140}=\frac{-6}{280}
=-3/140
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*140}=\frac{0}{280}
=0
$