Question

1. $7x^{2}-3x=10$

Explanation:

Step1: Rearrange to standard quadratic form

$7x^2 - 3x - 10 = 0$

Step2: Identify coefficients for quadratic formula

For $ax^2+bx+c=0$, $a=7$, $b=-3$, $c=-10$

Step3: Apply quadratic formula

$$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$
$$x=\frac{-(-3)\pm\sqrt{(-3)^2-4\times7\times(-10)}}{2\times7}$$

Step4: Calculate discriminant and simplify

$$x=\frac{3\pm\sqrt{9+280}}{14}=\frac{3\pm\sqrt{289}}{14}=\frac{3\pm17}{14}$$

Step5: Solve for two roots

$x_1=\frac{3+17}{14}=\frac{20}{14}=\frac{10}{7}$, $x_2=\frac{3-17}{14}=\frac{-14}{14}=-1$

Answer:

$x=-1$ or $x=\frac{10}{7}$