8-1/2y=1/4y-7

Solution for 8-1/2y=1/4y-7 equation:

8-1/2y=1/4y-7

We move all terms to the left:

8-1/2y-(1/4y-7)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: 4y-7)!=0

y∈R


We get rid of parentheses

-1/2y-1/4y+7+8=0

We calculate fractions


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

We add all the numbers together, and all the variables

(-4y)/8y^2+(-2y)/8y^2+15=0

We multiply all the terms by the denominator


(-4y)+(-2y)+15*8y^2=0

Wy multiply elements

120y^2+(-4y)+(-2y)=0

We get rid of parentheses

120y^2-4y-2y=0

We add all the numbers together, and all the variables

120y^2-6y=0

a = 120; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·120·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*120}=\frac{0}{240}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*120}=\frac{12}{240}
=1/20
$