Question

$5x^{2}-2x-10=0$

Explanation:

Step1: Identify quadratic coefficients

For $ax^2+bx+c=0$, here $a=5$, $b=-2$, $c=-10$

Step2: Apply quadratic formula

Quadratic formula: $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Step3: Calculate discriminant

$\Delta = b^2-4ac = (-2)^2 - 4(5)(-10) = 4 + 200 = 204$

Step4: Substitute into formula

$x=\frac{-(-2)\pm\sqrt{204}}{2(5)}=\frac{2\pm2\sqrt{51}}{10}$

Step5: Simplify the fraction

$x=\frac{1\pm\sqrt{51}}{5}$

Answer:

$x=\frac{1+\sqrt{51}}{5}$ or $x=\frac{1-\sqrt{51}}{5}$