2y+(4/6y)+3*4-5y=0

Solution for 2y+(4/6y)+3*4-5y=0 equation:

2y+(4/6y)+3*4-5y=0


Domain of the equation: 6y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

2y+(+4/6y)-5y+3*4=0

We add all the numbers together, and all the variables

-3y+(+4/6y)+12=0

We get rid of parentheses

-3y+4/6y+12=0

We multiply all the terms by the denominator


-3y*6y+12*6y+4=0

Wy multiply elements

-18y^2+72y+4=0

a = -18; b = 72; c = +4;
Δ = b2-4ac
Δ = 722-4·(-18)·4
Δ = 5472
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:

$\sqrt{\Delta}=\sqrt{5472}=\sqrt{144*38}=\sqrt{144}*\sqrt{38}=12\sqrt{38}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-12\sqrt{38}}{2*-18}=\frac{-72-12\sqrt{38}}{-36}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+12\sqrt{38}}{2*-18}=\frac{-72+12\sqrt{38}}{-36}
$