7(y+4)=4(2y+6)9y

Solution for 7(y+4)=4(2y+6)9y equation:

7(y+4)=4(2y+6)9y

We move all terms to the left:

7(y+4)-(4(2y+6)9y)=0

We multiply parentheses

7y-(4(2y+6)9y)+28=0


We calculate terms in parentheses: -(4(2y+6)9y), so:

4(2y+6)9y

We multiply parentheses

72y^2+216y

Back to the equation:

-(72y^2+216y)


We get rid of parentheses

-72y^2+7y-216y+28=0

We add all the numbers together, and all the variables

-72y^2-209y+28=0

a = -72; b = -209; c = +28;
Δ = b2-4ac
Δ = -2092-4·(-72)·28
Δ = 51745
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-209)-\sqrt{51745}}{2*-72}=\frac{209-\sqrt{51745}}{-144}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-209)+\sqrt{51745}}{2*-72}=\frac{209+\sqrt{51745}}{-144}
$