Question

Solve for x: 3 over 4 x + 5 over 8 = 4x. . x = __________________ Write your answer as a fraction in simplest form. Use the \"/\" symbol for the fraction bar

Answer 1

${ \frac{3}{4x} } + { \frac{5}{8} } = 4x \\ 3 + { \frac{5(4x)}{8} } = 4x(4x)$
$(8)3 + 20x = (8)16x^2$
$24 + 20x = 128x^2 \\ 128x^2 - 20x - 24 = 0 \\ 4(32x^2 - 5x - 6) = 0 \\ 32x^2 - 5x - 6 = 0$

$Solve\ using\ the\ formular\ \boxed{ x= { \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} } } \\ x= { \frac{-(-5) \pm \sqrt{(-5)^2 - 4(32)(-6)}}{2(32)} } \\ x= { \frac{5 \pm \sqrt{793}}{64} } \\ x = 0.51812\ or\ x=-0.36187$

$x$ cannot be written as a fraction.