Question

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1. (4х+3)*(6х+8)=0
2. (-х+3)*(2х+10)=0
3. (х+1/8)*(х-1/3)=0
4. 2х+3,5*(2х+6,8)=0

Answer 1

1.
$(4x + 3)(6x + 8) = 0 \\ {24x}^{2} + 32x + 18x + 24 = 0 \\ {24x}^{2} + 50x + 24 = 0 \\ a = 24 \\ b = 50 \\ c = 24 \\ d = {50}^{2} - 4 \times 24 \times 24 = 2500 - 2304 = 196 \\ \sqrt{d = 14 } \\ x1 = \frac{ - 50 - 14}{48} = \frac{ - 64}{48} = - \frac{4}{3} = - 1 \frac{1}{3} \\ x2 = \frac{ - 50 + 14}{48} = \frac{36}{48} = \frac{3}{4} = 0.75$

2.
$( - x + 3)(2x + 10) = 0 \\ - {2x}^{2} - 10x + 6x + 30 = 0 \\ - {2x}^{2} - 4x + 30 = 0 \\ a = - 2 \\ b = - 4 \\ c = 30 \\ d = {( - 4)}^{2} - 4 \times ( - 2) \times 30 = 16 + 240 = 256 \\ \sqrt{d = 16} \\ x1 = \frac{ 4 - 16}{ - 4} = - \frac{12}{4} = 3 \\ x2 = \frac{4 + 16}{ - 4} = \frac{20}{ - 4} = - 5$

3.
$(x + \frac{1}{8})( x - \frac{1}{3}) = 0 \\ {x}^{2} - \frac{1}{3} x + \frac{1}{8} x - \frac{1}{24} = 0 \\ {x}^{2} - \frac{5}{24} x - \frac{1}{24} = 0$
//Умножаем обе части на 24

$24 {x}^{2} - 5x - 1 = 0 \\ a = 24 \\ b = - 5 \\ c = - 1 \\ d = {( - 5)}^{2} - 4 \times 24 \times ( - 1) = 25 + 96 = 121 \\ \sqrt{d } = 11 \\ x1 = \frac{5 - 11}{48} = \frac{ - 6}{48} = - \frac{1}{8} \\ x2 = \frac{5 + 11}{48} = \frac{16}{48} = \frac{1}{3}$

4.
$2x + 3.5(2x + 6.8) = 0 \\ 2x + 7x + 23.8 = 0 \\ 9x = - 23.8 \\ x = - 23.8 \div 9 \\ x = - 23 \frac{8}{10} \div 9 \\ x = - \frac{238}{10} \times \frac{1}{9} \\ x = - \frac{119}{5} \times \frac{1}{9} \\ x = - \frac{119}{45} = - 2 \frac{29}{45} \\ x = - 2 \frac{29}{45}$