Answer:
x= 5
x= 8/3
Step-by-step explanation:
Step one
Given the expression
[tex]\frac{4}{3x+1} =\frac{x}{2x+10}[/tex]
cross multiply we have
[tex]4(2x+10)= x(3x+1)[/tex]
[tex]8x+40=3x^2+x[/tex]
collect like terms
[tex]3x^2+x-8x-40=0[/tex]
[tex]3x^2-7x-40=0[/tex]
applying the quadratic equation
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]x=\frac{-(-7)\pm\sqrt{(-7)^2-4*3(-40)}}{2*3}\\\\x=\frac{7\pm\sqrt{49+480}}{2*3}\\\\x=\frac{7\pm\sqrt{529}}{6}\\\\x=\frac{7\pm 23}{6}\\\\x=\frac{7\+23}{6}\\\\x=\frac{30}{6} \\\\x=5\\\\x=\frac{7-23}{6}\\\\x=\frac{-16}{6} \\\\x=\frac{8}{3}[/tex]
