2(7-1/4y)=4+1/3y

Solution for 2(7-1/4y)=4+1/3y equation:

2(7-1/4y)=4+1/3y

We move all terms to the left:

2(7-1/4y)-(4+1/3y)=0


Domain of the equation: 4y)!=0

y!=0/1

y!=0

y∈R



Domain of the equation: 3y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

2(-1/4y+7)-(1/3y+4)=0

We multiply parentheses

-2y-(1/3y+4)+14=0

We get rid of parentheses

-2y-1/3y-4+14=0

We multiply all the terms by the denominator


-2y*3y-4*3y+14*3y-1=0

Wy multiply elements

-6y^2-12y+42y-1=0

We add all the numbers together, and all the variables

-6y^2+30y-1=0

a = -6; b = 30; c = -1;
Δ = b2-4ac
Δ = 302-4·(-6)·(-1)
Δ = 876
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:

$\sqrt{\Delta}=\sqrt{876}=\sqrt{4*219}=\sqrt{4}*\sqrt{219}=2\sqrt{219}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{219}}{2*-6}=\frac{-30-2\sqrt{219}}{-12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{219}}{2*-6}=\frac{-30+2\sqrt{219}}{-12}
$