Answer
The solutions are $x=\dfrac{3}{4}\pm\dfrac{\sqrt{65}}{4}$
Work Step by Step
$(2x-5)(x+1)=2$
Evaluate the product on the left side:
$2x^{2}+2x-5x-5=2$
Take the $2$ to the left side:
$2x^{2}+2x-5x-5-2=0$
Simplify the left side:
$2x^{2}-3x-7=0$
Use the quadratic formula to solve this equation. The formula is $x=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$
In this case, $a=2$, $b=-3$ and $c=-7$
Substitute the known values into the formula and evaluate:
$x=\dfrac{-(-3)\pm\sqrt{(-3)^{2}-4(2)(-7)}}{2(2)}=\dfrac{3\pm\sqrt{9+56}}{4}=...$
$...=\dfrac{3\pm\sqrt{65}}{4}=\dfrac{3}{4}\pm\dfrac{\sqrt{65}}{4}$
