3x(x+3)=x+23 \\\\
3x^2+9x=x+23 \\\\
3x^2+9x-x-23=0 \\\\
3x^2+8x-23=0 \\\\
D=8^2-4\cdot 3\cdot (-23)=64+276=340=2\sqrt{85} \\\\
x_{1,2} = \dfrac{-8\pm 2\sqrt{85}}{6} \\\\
x_1 = \dfrac{-8+2\sqrt{85}}{6} = \dfrac{2(-4+\sqrt{85})}{6} = \dfrac{-4+\sqrt{85}}{3} \\\\
x_2=\dfrac{-8-2\sqrt{85}}{6} = \dfrac{2(-4-\sqrt{85})}{6} = \dfrac{-4-\sqrt{85}}{3}" alt="1. \; \; 6x(x+3)=2(x+23) \; \; \; \mid \; \div 2 \\\\
3x(x+3)=x+23 \\\\
3x^2+9x=x+23 \\\\
3x^2+9x-x-23=0 \\\\
3x^2+8x-23=0 \\\\
D=8^2-4\cdot 3\cdot (-23)=64+276=340=2\sqrt{85} \\\\
x_{1,2} = \dfrac{-8\pm 2\sqrt{85}}{6} \\\\
x_1 = \dfrac{-8+2\sqrt{85}}{6} = \dfrac{2(-4+\sqrt{85})}{6} = \dfrac{-4+\sqrt{85}}{3} \\\\
x_2=\dfrac{-8-2\sqrt{85}}{6} = \dfrac{2(-4-\sqrt{85})}{6} = \dfrac{-4-\sqrt{85}}{3}" align="absmiddle" class="latex-formula">
6-2t=3(4-t) \\\\
6-2t=12-3t \\\\
-2t+3t=12-6 \\\\
t=6" alt="3. \; \; 7(6-2t)=21(4-t) \; \; \; \mid \; \div \; 7 \\\\
6-2t=3(4-t) \\\\
6-2t=12-3t \\\\
-2t+3t=12-6 \\\\
t=6" align="absmiddle" class="latex-formula">
y(y-4)=2(y-8) \\\\
y^2-4y=2y-16 \\\\
y^2-4y-2y+16=0 \\\\
y^2-6y+16=0 \\\\
D=(-6)^2-4\cdot 1\cdot 16 = 36-64 = -28<0 \; \; , \; \; net \: korney." alt="2. \; \; 5y(y-4)=10(y-8) \; \; \; \mid \; \div \; 5 \\\\</p>
y(y-4)=2(y-8) \\\\
y^2-4y=2y-16 \\\\
y^2-4y-2y+16=0 \\\\
y^2-6y+16=0 \\\\
D=(-6)^2-4\cdot 1\cdot 16 = 36-64 = -28<0 \; \; , \; \; net \: korney." align="absmiddle" class="latex-formula">
6-2t=3(4-t) \\\\
6-2t=12-3t \\\\
-2t+3t=12-6 \\\\
t=6" alt="4. \; \; 7(6-2t)=21(4-t) \; \; \; \mid \; \div \; 7 \\\\
6-2t=3(4-t) \\\\
6-2t=12-3t \\\\
-2t+3t=12-6 \\\\
t=6" align="absmiddle" class="latex-formula">