6(2y+1)=46-4(3y2)

Solution for 6(2y+1)=46-4(3y2) equation:

6(2y+1)=46-4(3y^2)

We move all terms to the left:

6(2y+1)-(46-4(3y^2))=0

determiningTheFunctionDomain
-(46-43y^2)+6(2y+1)=0

We multiply parentheses

-(46-43y^2)+12y+6=0

We get rid of parentheses

43y^2+12y-46+6=0

We add all the numbers together, and all the variables

43y^2+12y-40=0

a = 43; b = 12; c = -40;
Δ = b2-4ac
Δ = 122-4·43·(-40)
Δ = 7024
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:

$\sqrt{\Delta}=\sqrt{7024}=\sqrt{16*439}=\sqrt{16}*\sqrt{439}=4\sqrt{439}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{439}}{2*43}=\frac{-12-4\sqrt{439}}{86}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{439}}{2*43}=\frac{-12+4\sqrt{439}}{86}
$