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

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

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

We move all terms to the left:

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


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R



Domain of the equation: 2y-7)!=0

y∈R


We get rid of parentheses

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

We calculate fractions


2y/8y^2+4y/8y^2+7+8=0

We add all the numbers together, and all the variables

2y/8y^2+4y/8y^2+15=0

We multiply all the terms by the denominator


2y+4y+15*8y^2=0

We add all the numbers together, and all the variables

6y+15*8y^2=0

Wy multiply elements

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