Answer:
x1 = -5
x2 = 3
Step-by-step explanation:
You have the following equation:
[tex]\frac{6}{x}-\frac{4}{5}=\frac{2x}{5}[/tex] (1)
To find the solutions of the equation (1) you first eliminate the denominators of the equation, by multiplying the m.c.m, which is 5x, as follow:
[tex]30-4x=2x^2[/tex]
Next, you write the previous equation in the general form ax^2 +bx+c=0, as follow:
[tex]2x^2+4x-30=0[/tex]
Next, you use the quadratic formula to find the solutions:
[tex]x_{1,2}=\frac{-b\pm \sqrt{b^2-4(a)(c)}}{2a}\\\\a=2;\ \ b=4;\ \ c=-30\\\\x_{1,2}=\frac{-4\pm \sqrt{4^2-4(2)(-30)}}{2(2)}\\\\x_{1,2}=\frac{-4\pm16}{4}\\\\x_1=-5\\\\x_2=3[/tex]
Then, the solutions for the given equation are x1=-5 and x2=3
