Chapter 9.5, Problem 35P

Solve each equation. If necessary, round to the nearest hundredth. If there is no solution, write no solution.

$5t^2-6t=35$

To determine

To solve : the equation

Answer to Problem 35P

The solution of the equation is $t=3.31,-2.11$

Explanation of Solution

Given information :

The equation is

  $5t^2-6t=35$

Formula used :

Sridhar Acharya  $\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Calculation :

The solution of the equation is

  $\begin{array}{l}5t^2-6t=35\\ 5t^2-6t-35=0\\ t=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\ t=\frac{-\left(-6\right)\pm \sqrt{{\left(-6\right)}^2-4\cdot 5\cdot \left(-35\right)}}{2\cdot 5}\text{ Where }b=-6,a=5,c=-35\\ t=\frac{6\pm \sqrt{36+700}}{10}\\ t=\frac{6\pm \sqrt{736}}{10}\\ t=\frac{6\pm 4\sqrt{46}}{10}\\ t=\frac{3\pm 2\sqrt{46}}{5}\\ t=\frac{3+2\sqrt{46}}{5},\frac{3-2\sqrt{46}}{5}\\ t=3.31,-2.11\end{array}$

Hence, the solution of the equation is $t=3.31,-2.11$ .