Solve the inequality 6x - 7 + x^2 > 0
Firstly rearrange the quadratic such that the coefficient of x2 is positive (already done in this example) and the quadratic is in the form of ax2 +bx + c, then solve for x, like you would solve a regular quadratic equation.
x2 + 6x - 7 > 0, (x + 7)(x - 1) > 0
This gives you the roots of this quadratic aka where the graph intersects the x axis. This is important as this tells you which values of x satisfy the inequality (would be best explained by drawing a quadratic graph). In this situation it is when the graph is above the x axis, so therefore be before the lowest root and after the highest root.
x = -7, x = +1
Therefore, x < -7, x > 1
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