Equations Formulas and Notes
Solving Equations
Quadratic Formula
The general quadratic equation is ax^{2}-bx+c=0 . x represents an
unknown, while a, b, and c are constants with a not equal to 0. Use the Quadratic formula to get the value of x.
Quadratic Formula: x = \frac{ - b \pm \sqrt{b^{2}-4ac} }{2a}
Example
Solve for x: 2x^{2}-3x-5=0
a = 2, b = -3, c = -5
x = \frac{ -b \pm \sqrt{b^{2}-4ac} }{2a}
x = \frac{ -(-3) \pm \sqrt{(-3)^{2}-4(2)(-5)} }{2(2)}
x = \frac{ 3 \pm \sqrt{(-3)^{2}-4(2)(-5)} }{2(2)}
x = \frac{ 3 \pm \sqrt{ 49 } }{ 4 }
x = \frac{ 3 \pm 7 }{ 4 }
x = \frac{ 3 + 7 }{ 4 } , x = \frac{ 3 - 7 }{ 4 }
x = 2.5 , x = -1
In \frac{ - b \pm \sqrt{ \Delta } }{2a}, \Delta = {b^{2}-4ac} .
If \Delta > 0 , there are two solutions.
If \Delta = 0 , there is only one solution.
If \Delta < 0 , there are no real solutions.
