Question

# Solve quadratic equation using the quadratic formula. 3x^2 - 3x - 4 = 0

Solve quadratic equation using the quadratic formula. $$\displaystyle{3}{x}^{{2}}-{3}{x}-{4}={0}$$

2020-11-25
The standard quadratic equation is: $$\displaystyle{a}{x}^{{2}}+{b}{x}+{c}={0}$$
Quadratic formula is: $$\displaystyle{x}=\frac{{−{b}\pm\sqrt{{{b}^{{2}}−{4}{a}{c}}}}}{{{2}{a}}}$$
Here, a=3, b=−3 and c=−4
So,
$$\displaystyle{x}=\frac{{-{3}{\left(-{3}\right)}\pm\sqrt{{{\left(-{3}\right)}^{{2}}-{4}\times{3}\times{\left(-{4}\right)}}}}}{{{2}\times{3}}}$$
$$\displaystyle{x}=\frac{{{3}\pm\sqrt{{{9}+{48}}}}}{{6}}$$
$$\displaystyle{x}=\frac{{{3}\pm\sqrt{{57}}}}{{6}}$$
Therefore, solutions are
$$\displaystyle{x}=\frac{{{3}+\sqrt{{57}}}}{{6}}{\quad\text{and}\quad}{x}=\frac{{{3}-\sqrt{{57}}}}{{6}}$$