12(y-34)62y-8(11y+7)=18y(-6-12)

Solution for 12(y-34)62y-8(11y+7)=18y(-6-12) equation:

12(y-34)62y-8(11y+7)=18y(-6-12)

We move all terms to the left:

12(y-34)62y-8(11y+7)-(18y(-6-12))=0

We add all the numbers together, and all the variables

12(y-34)62y-8(11y+7)-(18y(-18))=0

We multiply parentheses

744y^2-25296y-88y-(18y(-18))-56=0


We calculate terms in parentheses: -(18y(-18)), so:

18y(-18)

We multiply parentheses

-324y

Back to the equation:

-(-324y)


We add all the numbers together, and all the variables

744y^2-25384y-(-324y)-56=0

We get rid of parentheses

744y^2-25384y+324y-56=0

We add all the numbers together, and all the variables

744y^2-25060y-56=0

a = 744; b = -25060; c = -56;
Δ = b2-4ac
Δ = -250602-4·744·(-56)
Δ = 628170256
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:

$\sqrt{\Delta}=\sqrt{628170256}=\sqrt{16*39260641}=\sqrt{16}*\sqrt{39260641}=4\sqrt{39260641}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25060)-4\sqrt{39260641}}{2*744}=\frac{25060-4\sqrt{39260641}}{1488}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25060)+4\sqrt{39260641}}{2*744}=\frac{25060+4\sqrt{39260641}}{1488}
$