# Solve Using the Square Root Property 3x^2-15x-10=9

3×2-15x-10=9
Move all terms to the left side of the equation and simplify.
Move 9 to the left side of the equation by subtracting it from both sides.
3×2-15x-10-9=0
Subtract 9 from -10.
3×2-15x-19=0
3×2-15x-19=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=3, b=-15, and c=-19 into the quadratic formula and solve for x.
15±(-15)2-4⋅(3⋅-19)2⋅3
Simplify.
Simplify the numerator.
Raise -15 to the power of 2.
x=15±225-4⋅(3⋅-19)2⋅3
Multiply 3 by -19.
x=15±225-4⋅-572⋅3
Multiply -4 by -57.
x=15±225+2282⋅3
x=15±4532⋅3
x=15±4532⋅3
Multiply 2 by 3.
x=15±4536
x=15±4536
Simplify the expression to solve for the + portion of the ±.
Simplify the numerator.
Raise -15 to the power of 2.
x=15±225-4⋅(3⋅-19)2⋅3
Multiply 3 by -19.
x=15±225-4⋅-572⋅3
Multiply -4 by -57.
x=15±225+2282⋅3
x=15±4532⋅3
x=15±4532⋅3
Multiply 2 by 3.
x=15±4536
Change the ± to +.
x=15+4536
x=15+4536
Simplify the expression to solve for the – portion of the ±.
Simplify the numerator.
Raise -15 to the power of 2.
x=15±225-4⋅(3⋅-19)2⋅3
Multiply 3 by -19.
x=15±225-4⋅-572⋅3
Multiply -4 by -57.
x=15±225+2282⋅3
x=15±4532⋅3
x=15±4532⋅3
Multiply 2 by 3.
x=15±4536
Change the ± to -.
x=15-4536
x=15-4536
The final answer is the combination of both solutions.
x=15+4536,15-4536
The result can be shown in multiple forms.
Exact Form:
x=15+4536,15-4536
Decimal Form:
x=6.04729944…,-1.04729944…
Solve Using the Square Root Property 3x^2-15x-10=9