1/4y+2=-5/8y-5

Solution for 1/4y+2=-5/8y-5 equation:

1/4y+2=-5/8y-5

We move all terms to the left:

1/4y+2-(-5/8y-5)=0


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R



Domain of the equation: 8y-5)!=0

y∈R


We get rid of parentheses

1/4y+5/8y+5+2=0

We calculate fractions


8y/32y^2+20y/32y^2+5+2=0

We add all the numbers together, and all the variables

8y/32y^2+20y/32y^2+7=0

We multiply all the terms by the denominator


8y+20y+7*32y^2=0

We add all the numbers together, and all the variables

28y+7*32y^2=0

Wy multiply elements

224y^2+28y=0

a = 224; b = 28; c = 0;
Δ = b2-4ac
Δ = 282-4·224·0
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-28}{2*224}=\frac{-56}{448}
=-1/8
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+28}{2*224}=\frac{0}{448}
=0
$