9/2y-3/14y+3/14=3/4

Solution for 9/2y-3/14y+3/14=3/4 equation:

9/2y-3/14y+3/14=3/4

We move all terms to the left:

9/2y-3/14y+3/14-(3/4)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: 14y!=0

y!=0/14

y!=0

y∈R


We add all the numbers together, and all the variables

9/2y-3/14y+3/14-(+3/4)=0

We get rid of parentheses

9/2y-3/14y+3/14-3/4=0

We calculate fractions


(-1176y^2)/1568y^2+7056y/1568y^2+(-96y)/1568y^2+96y/1568y^2=0

We multiply all the terms by the denominator


(-1176y^2)+7056y+(-96y)+96y=0

We add all the numbers together, and all the variables

(-1176y^2)+7152y+(-96y)=0

We get rid of parentheses

-1176y^2+7152y-96y=0

We add all the numbers together, and all the variables

-1176y^2+7056y=0

a = -1176; b = 7056; c = 0;
Δ = b2-4ac
Δ = 70562-4·(-1176)·0
Δ = 49787136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49787136}=7056$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7056)-7056}{2*-1176}=\frac{-14112}{-2352}
=+6
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7056)+7056}{2*-1176}=\frac{0}{-2352}
=0
$