5/7(y)-1/14(y)=1

Solution for 5/7(y)-1/14(y)=1 equation:

5/7(y)-1/14(y)=1

We move all terms to the left:

5/7(y)-1/14(y)-(1)=0


Domain of the equation: 7y!=0

y!=0/7

y!=0

y∈R



Domain of the equation: 14y!=0

y!=0/14

y!=0

y∈R


We calculate fractions


70y/98y^2+(-7y)/98y^2-1=0

We multiply all the terms by the denominator


70y+(-7y)-1*98y^2=0

Wy multiply elements

-98y^2+70y+(-7y)=0

We get rid of parentheses

-98y^2+70y-7y=0

We add all the numbers together, and all the variables

-98y^2+63y=0

a = -98; b = 63; c = 0;
Δ = b2-4ac
Δ = 632-4·(-98)·0
Δ = 3969
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3969}=63$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(63)-63}{2*-98}=\frac{-126}{-196}
=9/14
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(63)+63}{2*-98}=\frac{0}{-196}
=0
$