2 real solutions
Step 1
reorder
[tex]\begin{gathered} 4x^2-8x+10=-x^2-54x \\ 4x^2+x^2-8x+10+54x=0 \\ 5x^2+46x+10=0 \\ \end{gathered}[/tex]Step 2
solve for x using the quadratic formula
[tex]\begin{gathered} 5x^2+46x+10=0 \\ x=\frac{-b\pm\sqrt[]{b^2}-4ac}{2a} \\ \text{replace} \\ x=\frac{-46\pm\sqrt[]{46^2}-4\cdot5\cdot10}{2\cdot5} \\ x=\frac{-46\pm\sqrt[]{46^2}-200}{2\cdot5}=\frac{-46\pm\sqrt[]{1916}}{10} \\ Hence \\ \\ \frac{x_{1=}-46+\sqrt[]{1916}}{10} \\ x_2=\frac{-46\pm\sqrt[]{1916}}{10} \end{gathered}[/tex]I hope this helps you
