# Solve for y 2y^2+20y+12=0

2y2+20y+12=0
Factor 2 out of 2y2+20y+12.
Factor 2 out of 2y2.
2(y2)+20y+12=0
Factor 2 out of 20y.
2(y2)+2(10y)+12=0
Factor 2 out of 12.
2y2+2(10y)+2⋅6=0
Factor 2 out of 2y2+2(10y).
2(y2+10y)+2⋅6=0
Factor 2 out of 2(y2+10y)+2⋅6.
2(y2+10y+6)=0
2(y2+10y+6)=0
Divide each term by 2 and simplify.
Divide each term in 2(y2+10y+6)=0 by 2.
2(y2+10y+6)2=02
Cancel the common factor of 2.
Cancel the common factor.
2(y2+10y+6)2=02
Divide y2+10y+6 by 1.
y2+10y+6=02
y2+10y+6=02
Divide 0 by 2.
y2+10y+6=0
y2+10y+6=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=1, b=10, and c=6 into the quadratic formula and solve for y.
-10±102-4⋅(1⋅6)2⋅1
Simplify.
Simplify the numerator.
Raise 10 to the power of 2.
y=-10±100-4⋅(1⋅6)2⋅1
Multiply 6 by 1.
y=-10±100-4⋅62⋅1
Multiply -4 by 6.
y=-10±100-242⋅1
Subtract 24 from 100.
y=-10±762⋅1
Rewrite 76 as 22⋅19.
Factor 4 out of 76.
y=-10±4(19)2⋅1
Rewrite 4 as 22.
y=-10±22⋅192⋅1
y=-10±22⋅192⋅1
Pull terms out from under the radical.
y=-10±2192⋅1
y=-10±2192⋅1
Multiply 2 by 1.
y=-10±2192
Simplify -10±2192.
y=-5±19
y=-5±19
The final answer is the combination of both solutions.
y=-5+19,-5-19
The result can be shown in multiple forms.
Exact Form:
y=-5+19,-5-19
Decimal Form:
y=-0.64110105…,-9.35889894…
Solve for y 2y^2+20y+12=0

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