In order to find the value of x, we need to replace y by 1.8 in the given expression:
[tex]\begin{gathered} y=-0.06x^2+0.7x+2.3 \\ \\ 1.8=-0.06x^2+0.7x+2.3 \\ \\ 1.8-1.8=-0.06x^2+0.7x+2.3-1.8 \\ \\ 0=-0.06x^2+0.7x+0.5 \\ \\ 0\cdot10=(-0.06x^2+0.7x+0.5)\cdot10 \\ \\ 0=-0.6x^2+7x+5 \\ \\ -0.6x^2+7x+5=0 \end{gathered}[/tex]Now, we can use the quadratic formula to find x:
[tex]\begin{gathered} x=\frac{-7\pm\sqrt[]{7^2-4\cdot(-0.6)\cdot5}}{2\cdot(-0.6)} \\ \\ x=\frac{-7\pm\sqrt[]{49+12}}{-1.2} \\ \\ x=\frac{-7\pm\sqrt[]{61}}{-1.2} \\ \\ x_1=\frac{-7-\sqrt[]{61}}{-1.2}\cong12.34 \\ \\ x_2=\frac{-7+\sqrt[]{61}}{-1.2}\cong-0.68 \end{gathered}[/tex]Therefore, x can have two different values, which are, approximately,
-0.68 foot and 12.34 feet.
