x(x-6)=4(x+6) Multiply out: x² - 6x = 4x + 24 x² - 6x - 4x - 24 = 0 x² - 10x - 24 = 0 This is a quadratic equation x² - 10x - 24 = 0 Divide through by 2 Multiply first and last coefficients: 1*-24 = -24 We look for two numbers that multiply to give -24, and add to give -10 Those two numbers are -12 and 2. Check: -12*2 = -24 2 + -12 = -10 We replace the middle term of -10x in the quadratic expression with 2x -12x x² - 10x - 24 = 0 x² + 2x - 12x - 24 = 0 x(x + 2) - 12(x + 2) = 0 (x + 2)(x - 12) = 0 x + 2 = 0 or x - 12 = 0 x = 0 -2 x = 0 + 12 x = -2 x = 12 The solutions are x = -2 or 12

x la patrat - 6x = 4x+24<=>x la a doua -10x-24=0 D= 100-4×1(-24) D=100+96 D=196 X1,2= 10 plus minus 14 : 2 <=>X1=10-14:2=-2 and X2= 10+14:2= 2