4-3y-(4-6y)*y=7

Solution for 4-3y-(4-6y)*y=7 equation:

4-3y-(4-6y)*y=7

We move all terms to the left:

4-3y-(4-6y)*y-(7)=0

We add all the numbers together, and all the variables

-3y-(-6y+4)*y+4-7=0

We add all the numbers together, and all the variables

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

We multiply parentheses

6y^2-3y-4y-3=0

We add all the numbers together, and all the variables

6y^2-7y-3=0

a = 6; b = -7; c = -3;
Δ = b2-4ac
Δ = -72-4·6·(-3)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-11}{2*6}=\frac{-4}{12}
=-1/3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+11}{2*6}=\frac{18}{12}
=1+1/2
$