3-y(7+2y)=4y

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

3-y(7+2y)=4y

We move all terms to the left:

3-y(7+2y)-(4y)=0

We add all the numbers together, and all the variables

-y(2y+7)-4y+3=0

We add all the numbers together, and all the variables

-4y-y(2y+7)+3=0

We multiply parentheses

-2y^2-4y-7y+3=0

We add all the numbers together, and all the variables

-2y^2-11y+3=0

a = -2; b = -11; c = +3;
Δ = b2-4ac
Δ = -112-4·(-2)·3
Δ = 145
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{-(-11)-\sqrt{145}}{2*-2}=\frac{11-\sqrt{145}}{-4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{145}}{2*-2}=\frac{11+\sqrt{145}}{-4}
$