The given expression is
[tex]4r^2+15r+7=-1[/tex]First, we add 1 on each side
[tex]\begin{gathered} 4r^2+15r+7+1=-1+1 \\ 4r^2+15r+8=0 \end{gathered}[/tex]Then, we use the quadratic formula
[tex]r=\frac{-b\pm\sqrt[]{b^2-4ac^{}}}{2a}[/tex]Where a = 4, b = 15, and c = 8.
[tex]\begin{gathered} r=\frac{-15\pm\sqrt[]{15^2-4\cdot4\cdot8}}{2\cdot4}=\frac{-15\pm\sqrt[]{225-128}}{8} \\ r=\frac{-15\pm\sqrt[]{97}}{8} \end{gathered}[/tex]Then, we rewrite the equation into two solutions
[tex]\begin{gathered} r_1=\frac{-15+\sqrt[]{97}}{8} \\ r_2=\frac{-15-\sqrt[]{97}}{8} \end{gathered}[/tex]