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Lucas Rezende · Answer 1 · 2023-08-16T16:50:42+0000

Given a quadratic equation with the following form

By the quadratic formula, the solutions are given by the following expression

$x_(\pm)=(-b\pm√(b^2-4ac))/(2a)$

In our problem we have the following equation

Therefore, our coefficients are

$\begin{gathered} a=4 \\ b=-7 \\ c=3 \end{gathered}$

Plugging those values into the quadratic formula, we have

$x_(\pm)=(-(-7)\pm√((-7)^2-4(4)(3)))/(2(4))$

Solving this equation, we have

$\begin{gathered} x_{\operatorname{\pm}}=(-(-7)\pm√((-7)^2-4(4)(3)))/(2(4)) \\ =(7\pm√(49-48))/(8) \\ =(7\pm1)/(8) \\ \implies\begin{cases}x_+={1} \\ x_-={(3)/(4)}=0.75\end{cases} \end{gathered}$

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