Eq with reciprocal

Solve given equation with reciprocal member:

a-6/a+10=4/8

Correct result:

a₁ =  0.5944
a₂ =  -10.0944

Solution:

$$\begin{gathered} a-6\mathrm{/}a+10=4\mathrm{/}8 \\ a-{\displaystyle \frac{6}{a}}+10={\displaystyle \frac{4}{8}} \\ a<>0 \\ {a}^2-6+10a=4\mathrm{/}8a \\ {a}^2-6+10a=4\mathrm{/}8a \\ {a}^2+9.5a-6=0 \\ p=1;q=9.5;r=-6 \\ D=q^2-4pr=9.5^2-4\cdot 1\cdot (-6)=114.25 \\ D>0 \\ {a}_{1,2}={\displaystyle \frac{-q\pm \sqrt{D}}{2p}}={\displaystyle \frac{-9.5\pm \sqrt{114.25}}{2}} \\ {a}_{1,2}=-4.75\pm 5.34438958161 \\ {a}_1=0.594389581608 \\ {a}_2=-10.0943895816 \\ \text{ Factored form of the equation: } \\ (a-0.594389581608)(a+10.0943895816)=0 \\ {a}_1=0.5944 \end{gathered}$$

Our quadratic equation calculator calculates it.

$a_2=(-10.0944)=-10.0944$

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