[tex]x + 4 - (2x - 3)(x - 4) = 0[/tex]
[tex]x + 4 - (2 {x}^{2} - 8x - 3x + 12) = 0[/tex]
[tex]x + 4 - 2 {x}^{2} + 8x + 3x - 12 = 0[/tex]
[tex] - 2 {x}^{2} + 12x - 8 = 0 \: | \div ( - 2)[/tex]
[tex] {x}^{2} - 6x + 4 = 0[/tex]
[tex]a = 1[/tex]
[tex]b = - 6[/tex]
[tex]c = 4[/tex]
[tex]\Delta = {b}^{2} - 4ac[/tex]
[tex]\Delta = {( - 6)}^{2} - 4 \times 1 \times 4[/tex]
[tex]\Delta = 36 - 16[/tex]
[tex]\Delta = 20[/tex]
[tex]x_{1,2}=\frac{-b\pm\sqrt{\Delta}}{2a}[/tex]
[tex]x_{1,2}=\frac{-( - 6)\pm\sqrt{20}}{2 \times 1}[/tex]
[tex]x_{1,2}=\frac{6\pm2\sqrt{5}}{2}[/tex]
[tex]x_{1}=\frac{6 + 2\sqrt{5}}{2}[/tex]
[tex]x_{1}=\frac{2(3+ \sqrt{5})}{2}[/tex]
[tex]x_{1}=3 + \sqrt{5}[/tex]
[tex]x_{2}=\frac{6 - 2\sqrt{5}}{2}[/tex]
[tex]x_{2}=\frac{2(3 - \sqrt{5})}{2}[/tex]
[tex]x_{2}=3 - \sqrt{5}[/tex]
