Question

solve: $5x+\frac{7}{2}=\frac{3}{2}x-14$

Answer 1

We have,

$5x+\frac{7}{2}=\frac{3}{2x}-14$

$5x-\frac{3}{2x}=-14-\frac{7}{2}$

$\frac{10x^2-3}{2x}=\frac{-28-7}{2}$

$10x^2-3=-35x$

$10x^2-3+35x=0$

$10x^2+35x-3=0$

Comparing that,

$a{x}^2+bx+c=0$

$a=10,b=35,c=-3$

Then, using quadratic formula

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$x=\frac{-35\pm \sqrt{{(-35)}^2-4\times 10\times (-3)}}{2a}$

$x=\frac{-35\pm \sqrt{1225+120}}{2\times 10}$

$x=\frac{-35\pm \sqrt{1345}}{20}$

$x=\frac{-35\pm \sqrt{1345}}{20}$

Hence, this is the answer.