-5y2-3y-4y=-2

Subtract 4y from -3y.

-5y2-7y=-2

Move 2 to the left side of the equation by adding it to both sides.

-5y2-7y+2=0

Factor -1 out of -5y2.

-(5y2)-7y+2=0

Factor -1 out of -7y.

-(5y2)-(7y)+2=0

Rewrite 2 as -1(-2).

-(5y2)-(7y)-1⋅-2=0

Factor -1 out of -(5y2)-(7y).

-(5y2+7y)-1⋅-2=0

Factor -1 out of -(5y2+7y)-1(-2).

-(5y2+7y-2)=0

-(5y2+7y-2)=0

Multiply each term in -(5y2+7y-2)=0 by -1.

-(5y2+7y-2)⋅-1=0⋅-1

Simplify -(5y2+7y-2)⋅-1.

Apply the distributive property.

(-(5y2)-(7y)–2)⋅-1=0⋅-1

Simplify.

Multiply 5 by -1.

(-5y2-(7y)–2)⋅-1=0⋅-1

Multiply 7 by -1.

(-5y2-7y–2)⋅-1=0⋅-1

Multiply -1 by -2.

(-5y2-7y+2)⋅-1=0⋅-1

(-5y2-7y+2)⋅-1=0⋅-1

Apply the distributive property.

-5y2⋅-1-7y⋅-1+2⋅-1=0⋅-1

Simplify.

Multiply -1 by -5.

5y2-7y⋅-1+2⋅-1=0⋅-1

Multiply -1 by -7.

5y2+7y+2⋅-1=0⋅-1

Multiply 2 by -1.

5y2+7y-2=0⋅-1

5y2+7y-2=0⋅-1

5y2+7y-2=0⋅-1

Multiply 0 by -1.

5y2+7y-2=0

5y2+7y-2=0

Use the quadratic formula to find the solutions.

-b±b2-4(ac)2a

Substitute the values a=5, b=7, and c=-2 into the quadratic formula and solve for y.

-7±72-4⋅(5⋅-2)2⋅5

Simplify the numerator.

Raise 7 to the power of 2.

y=-7±49-4⋅(5⋅-2)2⋅5

Multiply 5 by -2.

y=-7±49-4⋅-102⋅5

Multiply -4 by -10.

y=-7±49+402⋅5

Add 49 and 40.

y=-7±892⋅5

y=-7±892⋅5

Multiply 2 by 5.

y=-7±8910

y=-7±8910

The final answer is the combination of both solutions.

y=-7-8910,-7+8910

The result can be shown in multiple forms.

Exact Form:

y=-7-8910,-7+8910

Decimal Form:

y=0.24339811…,-1.64339811…

Solve for y -5y^2-3y-4y=-2