6y(y+8)=3(2y-7)

Solution for 6y(y+8)=3(2y-7) equation:

6y(y+8)=3(2y-7)

We move all terms to the left:

6y(y+8)-(3(2y-7))=0

We multiply parentheses

6y^2+48y-(3(2y-7))=0


We calculate terms in parentheses: -(3(2y-7)), so:

3(2y-7)

We multiply parentheses

6y-21

Back to the equation:

-(6y-21)


We get rid of parentheses

6y^2+48y-6y+21=0

We add all the numbers together, and all the variables

6y^2+42y+21=0

a = 6; b = 42; c = +21;
Δ = b2-4ac
Δ = 422-4·6·21
Δ = 1260
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:

$\sqrt{\Delta}=\sqrt{1260}=\sqrt{36*35}=\sqrt{36}*\sqrt{35}=6\sqrt{35}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-6\sqrt{35}}{2*6}=\frac{-42-6\sqrt{35}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+6\sqrt{35}}{2*6}=\frac{-42+6\sqrt{35}}{12}
$