[tex] {m}^{2} x + 3m - x = {m}^{2} + 2[/tex]
[tex]x = 5[/tex]
[tex] {m}^{2} \times 5 + 3m - 5 = {m}^{2} + 2[/tex]
[tex]5 {m}^{2} + 3m - 5 = {m}^{2} + 2[/tex]
[tex]5 {m}^{2} - {m}^{2} + 3m - 5 - 2 = 0[/tex]
[tex]4 {m}^{2} + 3m - 7 = 0[/tex]
[tex]a = 4[/tex]
[tex]b = 3[/tex]
[tex]c = - 7[/tex]
[tex]\Delta = {b}^{2} - 4ac[/tex]
[tex]\Delta = {3}^{2} - 4 \times 4 \times ( - 7)[/tex]
[tex]\Delta = 9 + 112[/tex]
[tex]\Delta = 121[/tex]
[tex]m_{1,2}=\frac{-b \: \pm \: \sqrt{\Delta}}{2a}[/tex]
[tex]m_{1,2}=\frac{-3 \: \pm \: \sqrt{121}}{2 \times 4}[/tex]
[tex]m_{1,2}=\frac{-3 \: \pm \: 11}{8}[/tex]
[tex]m_{1}=\frac{-3 \: + \: 11}{8}[/tex]
[tex]m_{1}=\frac{8}{8}[/tex]
[tex]m_{1}=1[/tex]
[tex]m_{2}=\frac{-3 \: - \: 11}{8}[/tex]
[tex]m_{2}= - \frac{14}{8}[/tex]
[tex]m_{2}= - \frac{7}{4}[/tex]
