-4y(6y-5)=23-3(8y+1)

Solution for -4y(6y-5)=23-3(8y+1) equation:

-4y(6y-5)=23-3(8y+1)

We move all terms to the left:

-4y(6y-5)-(23-3(8y+1))=0

We multiply parentheses

-24y^2+20y-(23-3(8y+1))=0


We calculate terms in parentheses: -(23-3(8y+1)), so:

23-3(8y+1)

determiningTheFunctionDomain
-3(8y+1)+23

We multiply parentheses

-24y-3+23

We add all the numbers together, and all the variables

-24y+20

Back to the equation:

-(-24y+20)


We get rid of parentheses

-24y^2+20y+24y-20=0

We add all the numbers together, and all the variables

-24y^2+44y-20=0

a = -24; b = 44; c = -20;
Δ = b2-4ac
Δ = 442-4·(-24)·(-20)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-4}{2*-24}=\frac{-48}{-48}
=1
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+4}{2*-24}=\frac{-40}{-48}
=5/6
$