1/2y+5-3/4y=0.

Solution for 1/2y+5-3/4y=0. equation:

1/2y+5-3/4y=0.


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R


We calculate fractions


4y/8y^2+(-6y)/8y^2+5=0

We multiply all the terms by the denominator


4y+(-6y)+5*8y^2=0

Wy multiply elements

40y^2+4y+(-6y)=0

We get rid of parentheses

40y^2+4y-6y=0

We add all the numbers together, and all the variables

40y^2-2y=0

a = 40; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·40·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*40}=\frac{0}{80}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*40}=\frac{4}{80}
=1/20
$