8y-5y/7y+1=5/4

Solution for 8y-5y/7y+1=5/4 equation:

8y-5y/7y+1=5/4

We move all terms to the left:

8y-5y/7y+1-(5/4)=0


Domain of the equation: 7y!=0

y!=0/7

y!=0

y∈R


We add all the numbers together, and all the variables

8y-5y/7y+1-(+5/4)=0

We get rid of parentheses

8y-5y/7y+1-5/4=0

We calculate fractions


8y+(-20y)/28y+(-35y)/28y+1=0

We multiply all the terms by the denominator


8y*28y+(-20y)+(-35y)+1*28y=0

Wy multiply elements

224y^2+(-20y)+(-35y)+28y=0

We get rid of parentheses

224y^2-20y-35y+28y=0

We add all the numbers together, and all the variables

224y^2-27y=0

a = 224; b = -27; c = 0;
Δ = b2-4ac
Δ = -272-4·224·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-27}{2*224}=\frac{0}{448}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+27}{2*224}=\frac{54}{448}
=27/224
$