4y-7+2y=-3y(y-1)-1

Solution for 4y-7+2y=-3y(y-1)-1 equation:

4y-7+2y=-3y(y-1)-1

We move all terms to the left:

4y-7+2y-(-3y(y-1)-1)=0

We add all the numbers together, and all the variables

6y-(-3y(y-1)-1)-7=0


We calculate terms in parentheses: -(-3y(y-1)-1), so:

-3y(y-1)-1

We multiply parentheses

-3y^2+3y-1

Back to the equation:

-(-3y^2+3y-1)


We get rid of parentheses

3y^2-3y+6y+1-7=0

We add all the numbers together, and all the variables

3y^2+3y-6=0

a = 3; b = 3; c = -6;
Δ = b2-4ac
Δ = 32-4·3·(-6)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-9}{2*3}=\frac{-12}{6}
=-2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+9}{2*3}=\frac{6}{6}
=1
$