8y+4(3+y)=3(y-7)10y

Solution for 8y+4(3+y)=3(y-7)10y equation:

8y+4(3+y)=3(y-7)10y

We move all terms to the left:

8y+4(3+y)-(3(y-7)10y)=0

We add all the numbers together, and all the variables

8y+4(y+3)-(3(y-7)10y)=0

We multiply parentheses

8y+4y-(3(y-7)10y)+12=0


We calculate terms in parentheses: -(3(y-7)10y), so:

3(y-7)10y

We multiply parentheses

30y^2-210y

Back to the equation:

-(30y^2-210y)


We add all the numbers together, and all the variables

12y-(30y^2-210y)+12=0

We get rid of parentheses

-30y^2+12y+210y+12=0

We add all the numbers together, and all the variables

-30y^2+222y+12=0

a = -30; b = 222; c = +12;
Δ = b2-4ac
Δ = 2222-4·(-30)·12
Δ = 50724
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:

$\sqrt{\Delta}=\sqrt{50724}=\sqrt{36*1409}=\sqrt{36}*\sqrt{1409}=6\sqrt{1409}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(222)-6\sqrt{1409}}{2*-30}=\frac{-222-6\sqrt{1409}}{-60}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(222)+6\sqrt{1409}}{2*-30}=\frac{-222+6\sqrt{1409}}{-60}
$