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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

-42y^2+63y-(y+4(y-4))=0


We calculate terms in parentheses: -(y+4(y-4)), so:

y+4(y-4)

We multiply parentheses

y+4y-16

We add all the numbers together, and all the variables

5y-16

Back to the equation:

-(5y-16)


We get rid of parentheses

-42y^2+63y-5y+16=0

We add all the numbers together, and all the variables

-42y^2+58y+16=0

a = -42; b = 58; c = +16;
Δ = b2-4ac
Δ = 582-4·(-42)·16
Δ = 6052
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:

$\sqrt{\Delta}=\sqrt{6052}=\sqrt{4*1513}=\sqrt{4}*\sqrt{1513}=2\sqrt{1513}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(58)-2\sqrt{1513}}{2*-42}=\frac{-58-2\sqrt{1513}}{-84}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(58)+2\sqrt{1513}}{2*-42}=\frac{-58+2\sqrt{1513}}{-84}
$