Final answer:
To find the real solutions of the equation 7x²+39x-18=0, use the quadratic formula, calculate the discriminant, and then solve for x substituting the values of a, b, and c.
Step-by-step explanation:
The real solutions of the equation 7x²+39x-18=0 can be found by using the quadratic formula, which solves any quadratic equation of the form ax²+bx+c = 0. The quadratic formula is given by x = (-b ± √(b²-4ac))/(2a). For our given equation, a is 7, b is 39, and c is -18.
First, we calculate the discriminant (Δ) which is b²-4ac. In this case, Δ = 39² - 4(7)(-18). After finding the discriminant, we can substitute a, b, and c into the quadratic formula and solve for the two possible values of x.