# Solve for y 0.3y^2+1.2y=-0.5 0.3y2+1.2y=-0.5
Move 0.5 to the left side of the equation by adding it to both sides.
0.3y2+1.2y+0.5=0
Factor 0.1 out of 0.3y2+1.2y+0.5.
Factor 0.1 out of 0.3y2.
0.1(3y2)+1.2y+0.5=0
Factor 0.1 out of 1.2y.
0.1(3y2)+0.1(12y)+0.5=0
Factor 0.1 out of 0.5.
0.1(3y2)+0.1(12y)+0.1(5)=0
Factor 0.1 out of 0.1(3y2)+0.1(12y).
0.1(3y2+12y)+0.1(5)=0
Factor 0.1 out of 0.1(3y2+12y)+0.1(5).
0.1(3y2+12y+5)=0
0.1(3y2+12y+5)=0
Divide each term by 0.1 and simplify.
Divide each term in 0.1(3y2+12y+5)=0 by 0.1.
0.1(3y2+12y+5)0.1=00.1
Cancel the common factor of 0.1.
3y2+12y+5=00.1
Divide 0 by 0.1.
3y2+12y+5=0
3y2+12y+5=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=3, b=12, and c=5 into the quadratic formula and solve for y.
-12±122-4⋅(3⋅5)2⋅3
Simplify.
Simplify the numerator.
Raise 12 to the power of 2.
y=-12±144-4⋅(3⋅5)2⋅3
Multiply 3 by 5.
y=-12±144-4⋅152⋅3
Multiply -4 by 15.
y=-12±144-602⋅3
Subtract 60 from 144.
y=-12±842⋅3
Rewrite 84 as 22⋅21.
Factor 4 out of 84.
y=-12±4(21)2⋅3
Rewrite 4 as 22.
y=-12±22⋅212⋅3
y=-12±22⋅212⋅3
Pull terms out from under the radical.
y=-12±2212⋅3
y=-12±2212⋅3
Multiply 2 by 3.
y=-12±2216
Simplify -12±2216.
y=-6±213
y=-6±213
The final answer is the combination of both solutions.
y=-6-213,-6+213
The result can be shown in multiple forms.
Exact Form:
y=-6-213,-6+213
Decimal Form:
y=-0.47247476…,-3.52752523…
Solve for y 0.3y^2+1.2y=-0.5

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