9(y-4)7y=5(3y-2)

Solution for 9(y-4)7y=5(3y-2) equation:

9(y-4)7y=5(3y-2)

We move all terms to the left:

9(y-4)7y-(5(3y-2))=0

We multiply parentheses

63y^2-252y-(5(3y-2))=0


We calculate terms in parentheses: -(5(3y-2)), so:

5(3y-2)

We multiply parentheses

15y-10

Back to the equation:

-(15y-10)


We get rid of parentheses

63y^2-252y-15y+10=0

We add all the numbers together, and all the variables

63y^2-267y+10=0

a = 63; b = -267; c = +10;
Δ = b2-4ac
Δ = -2672-4·63·10
Δ = 68769
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:

$\sqrt{\Delta}=\sqrt{68769}=\sqrt{81*849}=\sqrt{81}*\sqrt{849}=9\sqrt{849}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-267)-9\sqrt{849}}{2*63}=\frac{267-9\sqrt{849}}{126}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-267)+9\sqrt{849}}{2*63}=\frac{267+9\sqrt{849}}{126}
$