# Solve for y 4y^2+4y-24x+35=0

4y2+4y-24x+35=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=4, b=4, and c=-24x+35 into the quadratic formula and solve for y.
-4±42-4⋅(4⋅(-24x+35))2⋅4
Simplify.
Simplify the numerator.
Factor 4 out of 42-4⋅(4⋅(-24x+35)).
Factor 4 out of 42.
y=-4±4⋅4-4⋅(4⋅(-24x+35))2⋅4
Factor 4 out of -4⋅(4⋅(-24x+35)).
y=-4±4⋅4+4(-(4⋅(-24x+35)))2⋅4
Factor 4 out of 4⋅4+4(-(4⋅(-24x+35))).
y=-4±4(4-(4⋅(-24x+35)))2⋅4
y=-4±4(4-(4⋅(-24x+35)))2⋅4
Apply the distributive property.
y=-4±4(4-(4(-24x)+4⋅35))2⋅4
Multiply -24 by 4.
y=-4±4(4-(-96x+4⋅35))2⋅4
Multiply 4 by 35.
y=-4±4(4-(-96x+140))2⋅4
Apply the distributive property.
y=-4±4(4-(-96x)-1⋅140)2⋅4
Multiply -96 by -1.
y=-4±4(4+96x-1⋅140)2⋅4
Multiply -1 by 140.
y=-4±4(4+96x-140)2⋅4
Subtract 140 from 4.
y=-4±4(96x-136)2⋅4
Factor 8 out of 96x-136.
Factor 8 out of 96x.
y=-4±4(8(12x)-136)2⋅4
Factor 8 out of -136.
y=-4±4(8(12x)+8(-17))2⋅4
Factor 8 out of 8(12x)+8(-17).
y=-4±4(8(12x-17))2⋅4
y=-4±4⋅(8(12x-17))2⋅4
Multiply 4 by 8.
y=-4±32(12x-17)2⋅4
Rewrite 32(12x-17) as (22)2⋅(2(12x-17)).
Factor 16 out of 32.
y=-4±16(2)(12x-17)2⋅4
Rewrite 16 as 42.
y=-4±42⋅(2(12x-17))2⋅4
Rewrite 4 as 22.
y=-4±(22)2⋅(2(12x-17))2⋅4
Add parentheses.
y=-4±(22)2⋅(2(12x-17))2⋅4
y=-4±(22)2⋅(2(12x-17))2⋅4
Pull terms out from under the radical.
y=-4±222(12x-17)2⋅4
Raise 2 to the power of 2.
y=-4±42(12x-17)2⋅4
y=-4±42(12x-17)2⋅4
Multiply 2 by 4.
y=-4±42(12x-17)8
Simplify -4±42(12x-17)8.
y=-1±2(12x-17)2
y=-1±2(12x-17)2
The final answer is the combination of both solutions.
y=-1-2(12x-17)2
y=-1+2(12x-17)2
Solve for y 4y^2+4y-24x+35=0

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