Question

7. Solve the equation using the quadratic formula.
3x^2 = 2(2x+1)

Answer 1

Answer:

$\rm x = \dfrac{2+\sqrt{10}}{3},\dfrac{2-\sqrt{10}}{3}$

Step-by-step explanation:

A quadratic equation is given to us and we need to solve the equation using the quadratic formula . The given equation is ,

$\rm\implies 3x^2=2(2x+1)$

Open the brackets in RHS ,

$\rm\implies 3x^2= 4x + 2$

Transpose all the terms to LHS ,

$\rm\implies 3x^2-4x-2=0$

The general form of a quadratic equation is ax² + bx + c = 0 , and the roots of the equation by the Quadratic Formula ( Shreedhacharya's Formula ) is given by ,

$\rm\implies\red{ x =\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}}$

Using the quadratic formula , we have ,

$\rm\implies x =\dfrac{-(-4) \pm \sqrt{(-4)^2-4(3)(-2) }}{2(3)}$

Simplify ,

$\rm\implies x =\dfrac{4 \pm \sqrt{16+24 }}{6}$

$\rm\implies x = \dfrac{4\pm \sqrt{40}}{6}$

$\rm\implies x =\dfrac{4\pm 2\sqrt{10}}{6}$

$\rm\implies\boxed{\pink{\frak{ x = \dfrac{2+\sqrt{10}}{3},\dfrac{2-\sqrt{10}}{3}}}}$