Quadratic Formula Practice Worksheet

Practice solving quadratic equations using the quadratic formula with step-by-step solutions.

Use the quadratic formula to solve each equation. Simplify your answers whenever possible.

Quadratic Formula

\[ x= \frac{ -b \pm \sqrt{b^2-4ac} }{ 2a } \]
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Level 1: Basic Quadratics

Problem 1
\[ x^2 + 5x + 6 = 0 \]
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\(a=1,\ b=5,\ c=6\)

\[ x= \frac{ -5 \pm \sqrt{25-24} }{ 2 } \]
\[ x=-2,\ -3 \]
Problem 2
\[ x^2 - 7x + 10 = 0 \]
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\(a=1,\ b=-7,\ c=10\)

\[ x= \frac{ 7 \pm \sqrt{49-40} }{ 2 } \]
\[ x=5,\ 2 \]
Problem 3
\[ x^2 + 4x - 12 = 0 \]
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\(a=1,\ b=4,\ c=-12\)

\[ x= \frac{ -4 \pm \sqrt{16+48} }{ 2 } \]
\[ x= \frac{ -4 \pm 8 }{ 2 } \]
\[ x=2,\ -6 \]
Problem 4
\[ 2x^2 + 3x - 2 = 0 \]
Show solution

\(a=2,\ b=3,\ c=-2\)

\[ x= \frac{ -3 \pm \sqrt{9+16} }{ 4 } \]
\[ x= \frac{ -3 \pm 5 }{ 4 } \]
\[ x=\frac{1}{2},\ -2 \]

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