Rechner für quadratische Gleichungen

Your input: solve the quadratic equation $x^{2} - 14 x + 45 = 0$ by using quadratic formula.

The standard quadratic equation has the form $ax^2+bx+c=0$.

In our case, $a=1$, $b=-14$, $c=45$.

Now, find the discriminant using the formula $D=b^2-4ac$: $D=\left(-14\right)^2-4\cdot 1 \cdot 45=16$.

Find the roots of the equation using the formulas $x_1=\frac{-b-\sqrt{D}}{2a}$ and $x_2=\frac{-b+\sqrt{D}}{2a}$

$x_1=\frac{-\left(-14\right)-\sqrt{16}}{2\cdot 1}=5$ and $x_2=\frac{-\left(-14\right)+\sqrt{16}}{2\cdot 1}=9$

Answer: $x_1=5$; $x_2=9$