6(4+y)-3=4(y-3)2y

Solution for 6(4+y)-3=4(y-3)2y equation:

6(4+y)-3=4(y-3)2y

We move all terms to the left:

6(4+y)-3-(4(y-3)2y)=0

We add all the numbers together, and all the variables

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

We multiply parentheses

6y-(4(y-3)2y)+24-3=0


We calculate terms in parentheses: -(4(y-3)2y), so:

4(y-3)2y

We multiply parentheses

8y^2-24y

Back to the equation:

-(8y^2-24y)


We add all the numbers together, and all the variables

6y-(8y^2-24y)+21=0

We get rid of parentheses

-8y^2+6y+24y+21=0

We add all the numbers together, and all the variables

-8y^2+30y+21=0

a = -8; b = 30; c = +21;
Δ = b2-4ac
Δ = 302-4·(-8)·21
Δ = 1572
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:

$\sqrt{\Delta}=\sqrt{1572}=\sqrt{4*393}=\sqrt{4}*\sqrt{393}=2\sqrt{393}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{393}}{2*-8}=\frac{-30-2\sqrt{393}}{-16}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{393}}{2*-8}=\frac{-30+2\sqrt{393}}{-16}
$