Question

Solve the equation $5x^2-3x-4=0$ and give your answer correct to 3 significant figures:

Answer 1

Given equation:

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

Let us consider,

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

So, by using the formula, $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

So let, $b^2-4ac=D$

$x=\frac{-b\pm \sqrt{D}}{2a}$

$D=b^2-4ac$

$=(-3{)}^2-4(5\left)\right(-4)$

$=9+80$

$=89$

So,

$x=[-(-3)\pm \sqrt{89}]/2\left(5\right)$

$=[3\pm 9.43]/10$

$=[3+9.43]/10$ or $[3-9.43]/10$

$=12.433/10$ or $-6.43/10$

$=1.24$ or -0.643

$\therefore$ Value of $x=1.24$ or $-0.643$