Question

Calcule um número real tal que três vezes o quadrado desse número menos o dobro desse número seja igual a 40

Answer 1

$\Large\boxed{\begin{array}{l}\sf 3x^2-2x=40\\\sf 3x^2-2x-40=0\\\sf \Delta=b^2-4ac\\\sf\Delta=(-2)^2-4\cdot3\cdot(-40)\\\sf\Delta=4+480\\\sf\Delta=484\\\sf x=\dfrac{-b\pm\sqrt{\Delta}}{2a}\\\sf x=\dfrac{-(-2)\pm\sqrt{484}}{2\cdot3}\\\\\sf x=\dfrac{2\pm22}{6}\begin{cases}\sf x_1=\dfrac{2+22}{6}=\dfrac{24}{6}=4\\\\\sf x_2=\dfrac{2-22}{6}=-\dfrac{20}{6}=-\dfrac{10}{3}\end{cases}\end{array}}$