1/2y-3=3/4y-21

Solution for 1/2y-3=3/4y-21 equation:

1/2y-3=3/4y-21

We move all terms to the left:

1/2y-3-(3/4y-21)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: 4y-21)!=0

y∈R


We get rid of parentheses

1/2y-3/4y+21-3=0

We calculate fractions


4y/8y^2+(-6y)/8y^2+21-3=0

We add all the numbers together, and all the variables

4y/8y^2+(-6y)/8y^2+18=0

We multiply all the terms by the denominator


4y+(-6y)+18*8y^2=0

Wy multiply elements

144y^2+4y+(-6y)=0

We get rid of parentheses

144y^2+4y-6y=0

We add all the numbers together, and all the variables

144y^2-2y=0

a = 144; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·144·0
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*144}=\frac{0}{288}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*144}=\frac{4}{288}
=1/72
$