Question

Solve the equation $4x^2-5x-3=0$ and give your answer to correct two decimals.

Answer 1

Step 1 -Compare the equation with the general equation:

$4x^2-5x-3=0$

comparing the equation with the general equation $a{x}^2+bx+c=0$

$a=4,b=-5,c=-3$

Step 2-Find the discriminant of the equation:

$$\begin{gathered} d=b^2-4ac \\ d={(-5)}^2-4\times \left(4\right)\times (-3) \\ d=25+48 \\ d=73 \end{gathered}$$

Step 3-Find the roots of the equation:

$$\begin{gathered} x=\frac{-b\pm \sqrt{d}}{2a} \\ x=\frac{-(-5)\pm \sqrt{73}}{2\times 4} \\ x=\frac{5\pm 8.544}{8} \\ x=\frac{13.544}{8}andx=\frac{-3.544}{8} \\ x=1.693andx=-0.443 \\ x\approx 1.69andx\approx -0.44 \end{gathered}$$

Hence the solution of the equation is $x=1.69,-0.44$.