Pre-cal help pleaase?

Question

−3x^2 + 30x − 43=0

2x^2 + x − 6=0

Answer 1

−3x²+ 30x − 43=0

Multipy each side negative one

3x² - 30x + 43 = 0

quadratic equation form is ax² + bx + c =0 Then the roots of the equation is x1 = - b + √(b² -4ac) / 2

x2 = - b - √(b² -4ac) / 2a

Substitute a = 3, b = -30 and c = 43

Therefore the roots of the equation is x1 = [-(-30) + √[ (-30²)- 4(3)(43)] ] / 2(3)

x2 = [-(-30) - √[ (-30²) - 4(3)(43)] ] / 2(3)

Simplify

Therefore x1 = 30 + √( 900 - 516) / 6 or x2  = 30 -√( 900 - 516) / 6

x1 = [ 30 + √( 384 ) ] / 6  or  x2  = [ 30 - √( 384 ) ] / 6

x1 = [ 30 + √(64 × 6) ] / 6  or  x2 = 30 - √(64 × 6) ] / 6

x1 = [ 30 + 8√(6) ] / 6  or  x2 = [ 30 - 8√(6) ] / 6

Take  out common term 2.

x1 = [15 + 4√(6)] / 3 or x2 = [15 - 4√(6)] / 3

 

Answer 2

2x²+ x  - 6  = 0

2x² +4x -3x -6 =0

Take out common terms 2x and -3

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

Take out common term x + 2

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

x + 2 = 0 or 2x - 3 = 0

Substract  -2  from each side or Add 3 to each side

x = -2 or 2x = 3

Divide each side by 2

x = -2 or x = 3 / 2.