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