Question

6x^2+2x=3 round to the nearest hundreths

Answer 1

x= 0.56, x= -0.89

$6x^2+2x=3\\Simplify = 6x^2+2x-3=0\\\\\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\\quad x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\\mathrm{For\:}\quad a=6,\:b=2,\:c=-3:\quad x_{1,\:2}=\frac{-2\pm \sqrt{2^2-4\cdot \:6\left(-3\right)}}{2\cdot \:6}\\x=\frac{-2+\sqrt{2^2-4\cdot \:6\left(-3\right)}}{2\cdot \:6}:\quad \frac{-1+\sqrt{19}}{6}\\x=\frac{-2-\sqrt{2^2-4\cdot \:6\left(-3\right)}}{2\cdot \:6}:\quad -\frac{1+\sqrt{19}}{6}$

$x=\frac{-1+\sqrt{19}}{6},\:x=-\frac{1+\sqrt{19}}{6}$