7/4y+16=9/7y-10

Solution for 7/4y+16=9/7y-10 equation:

7/4y+16=9/7y-10

We move all terms to the left:

7/4y+16-(9/7y-10)=0


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R



Domain of the equation: 7y-10)!=0

y∈R


We get rid of parentheses

7/4y-9/7y+10+16=0

We calculate fractions


49y/28y^2+(-36y)/28y^2+10+16=0

We add all the numbers together, and all the variables

49y/28y^2+(-36y)/28y^2+26=0

We multiply all the terms by the denominator


49y+(-36y)+26*28y^2=0

Wy multiply elements

728y^2+49y+(-36y)=0

We get rid of parentheses

728y^2+49y-36y=0

We add all the numbers together, and all the variables

728y^2+13y=0

a = 728; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·728·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*728}=\frac{-26}{1456}
=-1/56
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*728}=\frac{0}{1456}
=0
$