Question

Please solve this equations

Answer 1

(1) x²-3x-18 = 0
x² +3x - 6x - 18 = 0
x(x+3) - 6(x+3) = 0
(x+3)(x-6) = 0
x+3 = 0 => x = -3
x-6 = 0 => x = 6

(2) 5x² - 3x - 2 = 0
5x² - 5x + 2x - 2 = 0
5x(x-1)+2(x-1) = 0
(5x+2) (x-1) = 0
5x+2 = 0 => x = -2/5
x-1 = 0 => x = 1

(3) (6x+5)/(4x+7) = (x+5)/(2x+6)
(6x+5)(2x+6) = (x+5)(4x+7)
12x² + 36x + 10x + 30 = 4x² + 7x + 20x + 35
12x² + 46x + 30 = 4x² + 27x + 35
12x² - 4x² + 46x - 27x + 30 - 35 = 0
8x² + 19x - 5 = 0
a = 8,b = 19,c = -5
discriminant = b²-4ac = 19² - 4(8)(-5)
= 361 + 160
= 520
b²-4ac > 0
x = -b ± √b²-4ac/2a
x = -19 ± √520/2(8)
x = (-19±2√130)/16

Therefore, x = (-19+2√130)/16 and (-19-2√130)/16

hope it's helpful …