# Solve for q 5q^2-3q=4a^2-5q+15

5q2-3q=4a2-5q+15
Move all terms containing q to the left side of the equation.
Add 5q to both sides of the equation.
5q2-3q+5q=4a2+15
Add -3q and 5q.
5q2+2q=4a2+15
5q2+2q=4a2+15
Move all the expressions to the left side of the equation.
Move 4a2 to the left side of the equation by subtracting it from both sides.
5q2+2q-4a2=15
Move 15 to the left side of the equation by subtracting it from both sides.
5q2+2q-4a2-15=0
5q2+2q-4a2-15=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=5, b=2, and c=-4a2-15 into the quadratic formula and solve for q.
-2±22-4⋅(5⋅(-4a2-15))2⋅5
Simplify.
Simplify the numerator.
Raise 2 to the power of 2.
q=-2±4-4⋅(5⋅(-4a2-15))2⋅5
Apply the distributive property.
q=-2±4-4⋅(5(-4a2)+5⋅-15)2⋅5
Multiply -4 by 5.
q=-2±4-4⋅(-20a2+5⋅-15)2⋅5
Multiply 5 by -15.
q=-2±4-4⋅(-20a2-75)2⋅5
Apply the distributive property.
q=-2±4-4(-20a2)-4⋅-752⋅5
Multiply -20 by -4.
q=-2±4+80a2-4⋅-752⋅5
Multiply -4 by -75.
q=-2±4+80a2+3002⋅5
Add 4 and 300.
q=-2±80a2+3042⋅5
Factor 16 out of 80a2+304.
Factor 16 out of 80a2.
q=-2±16(5a2)+3042⋅5
Factor 16 out of 304.
q=-2±16(5a2)+16(19)2⋅5
Factor 16 out of 16(5a2)+16(19).
q=-2±16(5a2+19)2⋅5
q=-2±16(5a2+19)2⋅5
Rewrite 16(5a2+19) as (22)2(5a2+19).
Rewrite 16 as 42.
q=-2±42(5a2+19)2⋅5
Rewrite 4 as 22.
q=-2±(22)2(5a2+19)2⋅5
q=-2±(22)2(5a2+19)2⋅5
Pull terms out from under the radical.
q=-2±225a2+192⋅5
Raise 2 to the power of 2.
q=-2±45a2+192⋅5
q=-2±45a2+192⋅5
Multiply 2 by 5.
q=-2±45a2+1910
Simplify -2±45a2+1910.
q=-1±25a2+195
q=-1±25a2+195
The final answer is the combination of both solutions.
q=-1-25a2+195
q=-1+25a2+195
Solve for q 5q^2-3q=4a^2-5q+15

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