Answer:
x = 1.434 and x=0.232
Step-by-step explanation:
To find the root of the equation stated above we need to:
(1) Write the polynomial equation with zero on the right hand side:
[tex]3x^{2} + 1 = 5x[/tex] ⇒ [tex]3x^{2} -5x + 1 = 0[/tex]
(2) Divide the whole equation by 3
[tex]3x^{2} -5x + 1 = 0[/tex] ⇒ [tex]x^{2} -\frac{5}{3}x + \frac{1}{3}= 0[/tex]
(3) Use the quadratic formula to solve the quadratic equation:
The quadratic formula states that the two solutions for a quadratic equation is given by:
[tex]\frac{-b±\sqrt{b^{2} - 4ac}}{2a}[/tex] (1)
In this case, a = 1, b = [tex]-\frac{5}{3}, c= \frac{1}{3}[/tex]
Substituiting a, b and c in equation (1) We get:
[tex]\frac{-\frac{5}{3}±\sqrt{(-\frac{5}{3})^{2} - 4(1)(\frac{1}{3})}}{2(1)}[/tex] (1)
The two solutions are:
x = 1.434 and x=0.232
