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

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

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

We move all terms to the left:

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


We calculate terms in parentheses: -(-3y(2y+7)), so:

-3y(2y+7)

We multiply parentheses

-6y^2-21y

Back to the equation:

-(-6y^2-21y)


We get rid of parentheses

6y^2+21y-2y+3=0

We add all the numbers together, and all the variables

6y^2+19y+3=0

a = 6; b = 19; c = +3;
Δ = b2-4ac
Δ = 192-4·6·3
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-17}{2*6}=\frac{-36}{12}
=-3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+17}{2*6}=\frac{-2}{12}
=-1/6
$