So firstly, you want to multiply x on each side of the equation: [tex] 3x^2+4x=1 [/tex]
Next, subtract 1 on each side: [tex] 3x^2+4x-1=0 [/tex]
Next, we will be using the quadratic formula, which is [tex] x=\frac{-b+/-\sqrt{b^2-4ac}}{2a} [/tex] , with a = x^2 coefficient, b = x coefficient, and c = constant. Our equation will look like this: [tex] x=\frac{-4+/-\sqrt{4^2-4*3*(-1)}}{2*3} [/tex]
Firstly, solve the exponents and multiplications: [tex] x=\frac{-4+/-\sqrt{16+12}}{6} [/tex]
Next, do the addition, and your exact solutions are: [tex] x=\frac{-4+\sqrt{28}}{6} [/tex] and [tex] x=\frac{-4-\sqrt{28}}{6} [/tex]
