[tex] \frac{ {x}^{2} + 3x}{ 2} = \frac{x + 7}{4} \: \: \: \: | \times 4 \\ 2( {x}^{2} + 3x) = x + 7 \\ 2 {x}^{2} + 6x = x + 7 \\ 2 {x}^{2} + 5x - 7 = 0 \\ d = 5 {}^{2} - 4 \times 2 \times ( - 7) = 25 + 56 = 81 \\ x_{1} = \frac{ - 5 + 9}{2 \times 2} = \frac{4}{4} = 1 \\ x_{2} = \frac{ - 5 - 9}{2 \times 2} = - \frac{14}{4} = - \frac{7}{2} = -3.5[/tex]