1/2y+21/4-5/8y-43/4=0

Solution for 1/2y+21/4-5/8y-43/4=0 equation:

1/2y+21/4-5/8y-43/4=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: 8y!=0

y!=0/8

y!=0

y∈R


We calculate fractions


(-5504y^2+21)/256y^2+128y/256y^2+(-160y)/256y^2=0

We multiply all the terms by the denominator


(-5504y^2+21)+128y+(-160y)=0

We get rid of parentheses

-5504y^2+128y-160y+21=0

We add all the numbers together, and all the variables

-5504y^2-32y+21=0

a = -5504; b = -32; c = +21;
Δ = b2-4ac
Δ = -322-4·(-5504)·21
Δ = 463360
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{463360}=\sqrt{256*1810}=\sqrt{256}*\sqrt{1810}=16\sqrt{1810}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-16\sqrt{1810}}{2*-5504}=\frac{32-16\sqrt{1810}}{-11008}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+16\sqrt{1810}}{2*-5504}=\frac{32+16\sqrt{1810}}{-11008}
$