4/7y=8-2/4y+10

Solution for 4/7y=8-2/4y+10 equation:

4/7y=8-2/4y+10

We move all terms to the left:

4/7y-(8-2/4y+10)=0


Domain of the equation: 7y!=0

y!=0/7

y!=0

y∈R



Domain of the equation: 4y+10)!=0

y∈R


We add all the numbers together, and all the variables

4/7y-(-2/4y+18)=0

We get rid of parentheses

4/7y+2/4y-18=0

We calculate fractions


16y/28y^2+14y/28y^2-18=0

We multiply all the terms by the denominator


16y+14y-18*28y^2=0

We add all the numbers together, and all the variables

30y-18*28y^2=0

Wy multiply elements

-504y^2+30y=0

a = -504; b = 30; c = 0;
Δ = b2-4ac
Δ = 302-4·(-504)·0
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-30}{2*-504}=\frac{-60}{-1008}
=5/84
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+30}{2*-504}=\frac{0}{-1008}
=0
$