Solve each quadratic inequality by using a graph, a table, or algebraically.

$-3x^2+10x<5$

Solution

VerifiedTo find the solution for the given inequality, start by finding the roots of the related function.

$\boxed{\color{#4257b2}x = \dfrac{-b \pm \sqrt{b^{2} - 4ac}}{2a}}$

$\begin{align*} & a = -3; b = 10; c = -5 && {\text{Identify $a$, $b$ and $c$ from the given equation}}\\ x &= \dfrac{-10 \pm \sqrt{10^{2} - 4(-3)(-5)}}{2(-3)} && {\text{Substitute the values}}\\ x &= \dfrac{-10 \pm \sqrt{100 - 60}}{-6} && {\text{Evaluate the power and multiply}}\\ x &= \dfrac{-10 \pm \sqrt{40}}{-6} && {\text{Subtract the values inside the radical sign}}\\ x &= \dfrac{-10 \pm \sqrt{2^{2} \cdot 10}}{-6} && {\text{Factor as perfect square}}\\ x &= \dfrac{-10 \pm 2 \sqrt{10}}{-6} && {\text{Extract the square root}}\\ x = \dfrac{-10 + 2 \sqrt{10}}{-6} &{\text{ or }} x = \dfrac{-10 - 2 \sqrt{10}}{-6} && {\text{Show as 2 equations}}\\ \color{#4257b2}\boldsymbol{x \approx 0.61} &{\textbf{ or }} \color{#4257b2}\boldsymbol{x \approx 2.72} && {\text{Simplify}} \end{align*}$

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