How do you solve an equation like x^2+3x-4=0

There are many ways of solving this equation, which is called a second order polynomial (where the order describes the highest power of x), let's focus on the most general for now: the quadratic formula. 

For any equation of the form ax²+bx+c=0, we can use this formula to find values of x for which this equation is satisfied. Start by calculating the discriminant of our equation, given by D = b²-4ac. If D is bigger than 0, than we can apply the quadratic formula. In our example, a=1, b=3 and c=-4, which means D=3²-(-4*4)=9+16=25, which is bigger than 1, so it works! 

The values of x can then be found using the quadratic formula, 

x₁=(-b+(squareroot(D))/(2a)

x₂=(-b-(squareroot(D))/(2a)

Notice the difference between those two formulas is the + and - in front of the square root of D. 

For our example, this would give: 

x₁=(-3+(squareroot(25))/(2*1)=(-3+5)/2=1

x₂=(-3-(squareroot(25))/(2*1)=(-3-5)/2=-4

You can check that this is correct by replacing x with one of your values and verify is does equal 0!