Solve x2 x 6 by factoring 3 Solve the following equations

Solve x^2 + x = 6 by factoring. 3. Solve the following equations: 10/x + 4 = 12/x - 3 3x^2 + 7x - 4 = 0 squareroot 5 - x + 1 = x - 2

2) x^2 + x = 6

subtracting 6 from both sides

x^2 + x - 6 = 0

x^2 +3x - 2x - 6 = 0

(x+3) (x-2) = 0

x+3 = 0

x = -3

x-2 = 0

x = 2

3) a) (10/x) + 4 = {12 / (x-3 )}

multiplying entire equation by x(x-3)

10(x-3) + 4 x(x-3) = 12x

10x - 30 +4x^2 -12x = 12x

4x^2 -14x - 30 = 0

or 2x^2 -7x - 15 = 0

(2x+3)(x-5) = 0

x = -3/2

x = 5

b) 3x^2 + 7x - 4 = 0

applying quadratic formula to solve

a = 3 , b = 7 , c = -4

x = { -b +- sqrt (b^2 -4ac ) } / 2a

plugging the values in the formula we get

x = { -7 +- sqrt ( 49 - 4*3*-4) } / 2*3

x = (-7 + sqrt 97 ) / 6

x = ( -7 - sqrt 97 ) / 6