7/8y-9=3/5y+5

Solution for 7/8y-9=3/5y+5 equation:

7/8y-9=3/5y+5

We move all terms to the left:

7/8y-9-(3/5y+5)=0


Domain of the equation: 8y!=0

y!=0/8

y!=0

y∈R



Domain of the equation: 5y+5)!=0

y∈R


We get rid of parentheses

7/8y-3/5y-5-9=0

We calculate fractions


35y/40y^2+(-24y)/40y^2-5-9=0

We add all the numbers together, and all the variables

35y/40y^2+(-24y)/40y^2-14=0

We multiply all the terms by the denominator


35y+(-24y)-14*40y^2=0

Wy multiply elements

-560y^2+35y+(-24y)=0

We get rid of parentheses

-560y^2+35y-24y=0

We add all the numbers together, and all the variables

-560y^2+11y=0

a = -560; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-560)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-560}=\frac{-22}{-1120}
=11/560
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-560}=\frac{0}{-1120}
=0
$