Solve the equation. 5x^{2}=2x-3

DofotheroU 2021-09-30 Answered
Solve the equation.
\(\displaystyle{5}{x}^{{{2}}}={2}{x}-{3}\)

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Expert Answer

ensojadasH
Answered 2021-10-01 Author has 6526 answers
Step 1
Given: \(\displaystyle{5}{x}^{{{2}}}={2}{x}-{3}\)
For finding solution of given equation, we do transportation then by using quadratic formula find the solution of given equation
So,
\(\displaystyle{5}{x}^{{{2}}}-{2}{x}+{3}={0}\)...(1)
We know that solution of quadratic equation \(\displaystyle{\left({a}{x}^{{{2}}}+{b}{x}+{c}={0}\right)}\) is given by
\(\displaystyle{x}={\frac{{-{b}\pm\sqrt{{{b}^{{{2}}}-{4}{a}{c}}}}}{{{2}{a}}}}\)...(2)
Step 2
So, by using equation(2) solution of given equation will be
\(\displaystyle{x}={\frac{{-{\left(-{2}\right)}\pm\sqrt{{{\left(-{2}\right)}^{{{2}}}-{4}{\left({5}\right)}{\left({3}\right)}}}}}{{{2}{\left({5}\right)}}}}\)
\(\displaystyle={\frac{{{4}\pm\sqrt{{{4}-{60}}}}}{{{10}}}}\)
\(\displaystyle={\frac{{{4}\pm\sqrt{{-{56}}}}}{{{10}}}}\)
\(\displaystyle={\frac{{{4}\pm{2}\sqrt{{{14}}}{i}}}{{{10}}}}\)
Hence, solution of given equation is \(\displaystyle{x}={\frac{{{4}\pm{2}\sqrt{{{14}}}{i}}}{{{10}}}}\).
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