# Using quadratic formula to solve quadratic equations

##### Intros

##### Examples

###### Lessons

**Solving a quadratic equation with TWO REAL SOLUTIONS**

Solve using the quadratic formula: $x^2+10x+6=0$**Solving a quadratic equation with ONE (REPEATED) REAL SOLUTION**

Solve using the quadratic formula: $9x^2+25=30x$**Solving a quadratic equation with TWO COMPLEX SOLUTIONS**

Solve using the quadratic formula: $-3x^2-24x=49$

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###### Topic Notes

Not sure if you should solve the quadratic equation by factoring or completing the square? No worries. You can always use the quadratic formula. The beauty of the quadratic formula is that it can always give you the answer no matter if the quadratic equations can be factored or not.

__Quadratic Formula__For the quadratic equation: $a{x^2} + bx + c = 0$

the solutions are: $x = \frac{{ - b\; \pm \;\sqrt {{b^2} - 4ac} }}{{2a}}$

###### Basic Concepts

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