Solving Quadratic Equations Using the Quadratic
Formula
Example
Solve using the quadratic formula: 10  5x^{2} = 6x
Solution
Step 1 Write the quadratic equation in standard form,
ax^{2} + bx + c = 0.
Subtract 6x from both sides of the equation.
On the left side, write the terms in
decreasing powers of x.
Step 2 Identify the values of a, b, and c. 
105x2 = 6x

Step 3 Substitute the values of a,
b, and c into the quadratic
formula. 

Step 4 Simplify. 

Simplify the radical.


Factor 2 from the numerator
and denominator.
Reduce by canceling the
common factor, 2
Step 5 Check each solution.
We leave the check to you. 

The two solutions of 10  5x^{2} = 6x are
Note:
Hereâ€™s another way to simplify: 

Factor out 2. 

Multiply by


(We multiplied by
because we do not
want a negative sign in the denominator.)
