3(5y+2)-y=2(y-3)y=-1

Solution for 3(5y+2)-y=2(y-3)y=-1 equation:

3(5y+2)-y=2(y-3)y=-1

We move all terms to the left:

3(5y+2)-y-(2(y-3)y)=0

We add all the numbers together, and all the variables

-1y+3(5y+2)-(2(y-3)y)=0

We multiply parentheses

-1y+15y-(2(y-3)y)+6=0


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

2(y-3)y

We multiply parentheses

2y^2-6y

Back to the equation:

-(2y^2-6y)


We add all the numbers together, and all the variables

14y-(2y^2-6y)+6=0

We get rid of parentheses

-2y^2+14y+6y+6=0

We add all the numbers together, and all the variables

-2y^2+20y+6=0

a = -2; b = 20; c = +6;
Δ = b2-4ac
Δ = 202-4·(-2)·6
Δ = 448
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:

$\sqrt{\Delta}=\sqrt{448}=\sqrt{64*7}=\sqrt{64}*\sqrt{7}=8\sqrt{7}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-8\sqrt{7}}{2*-2}=\frac{-20-8\sqrt{7}}{-4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+8\sqrt{7}}{2*-2}=\frac{-20+8\sqrt{7}}{-4}
$