Solve for x in the equation 2x^2+3x-7=x^2+5x+39

Subtract x^2 from both sides

x^2 + 3x - 7 = 5x + 39

Subtract 5x from both sides

x^2 - 2x - 7 = 39

Add 7 to both sides

x^2 - 2x = 46

Complete the square by adding (b/2) ^2 to both sides, b = (-2)

(-2/2) = - 1, then square that (-1) ^2 = 1

x^2 - 2x + 1 = 46 + 1

Simplify the expression by factoring

(x - 1) ^2 = 47

Take square root on each side

x - 1 = (sqrt (47))

Solve for x

x = 1 + (sqrt (47))

Since 47 is prime, 47 cannot be broken down by the square root and this is the answer to your problem.