[tex]2x^2-x=21\\\\\implies 2x^2 -x -21 =0\\\\\text{Apply quadratic formula},~ x = \dfrac{-b \pm \sqrt{b^2 -4ac}}{2a}\\\\\text{In this case,}~ a =2 , b =-1, c =-21}\\\\\implies x = \dfrac{-(-1) \pm \sqrt{(-1)^2 - 4\cdot 2 \cdot (-21)}}{2(2)}\\\\\implies x =\dfrac{1 \pm \sqrt{169}}{4}\\\\\\\implies x = \dfrac{ 1 \pm 13}4\\\\\\\text{Hence,}\\\\x =\dfrac{1+13}4 = \dfrac{14}4 = \dfrac 72\\\\\text{or}\\\\x =\dfrac{1-13}4 = -\dfrac{12}4 =-3[/tex]
