Answer
The solutions are $x=\dfrac{7}{2}\pm\dfrac{\sqrt{61}}{2}$
Work Step by Step
$x(x-7)=3$
Evaluate the product on the left side of the equation:
$x^{2}-7x=3$
Take $3$ to the left side:
$x^{2}-7x-3=0$
Use the quadratic formula to solve this equation. The formula is $x=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$
In this case, $a=1$, $b=-7$ and $c=-3$
Substitute the known values into the formula and evaluate:
$x=\dfrac{-(-7)\pm\sqrt{(-7)^{2}-4(1)(-3)}}{2(1)}=\dfrac{7\pm\sqrt{49+12}}{2}=...$
$...=\dfrac{7\pm\sqrt{61}}{2}=\dfrac{7}{2}\pm\dfrac{\sqrt{61}}{2}$
