Solve x/43x-2 / 2 = x-3/2 - ScanMath

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Type your math problem... x/43x-2 / 2 = x-3/2

Question

Solve the equation

x_{1} = \frac{43 - 1763}{2}, x_{2} = \frac{43 + 1763}{2}

Alternative Form

x_{1} \approx 0.505953, x_{2} \approx 42.494047

Evaluate

\frac{x}{43} x - \frac{2}{2} = x - \frac{3}{2}

Simplify

More Steps

\frac{x ^{2}}{43} - 1 = x - \frac{3}{2}

Multiply both sides of the equation by LCD

(\frac{x ^{2}}{43} - 1) \times 86 = (x - \frac{3}{2}) \times 86

Simplify the equation

More Steps

2 x^{2} - 86 = (x - \frac{3}{2}) \times 86

Simplify the equation

More Steps

2 x^{2} - 86 = 86 x - 129

Move the expression to the left side

2 x^{2} - 86 - (86 x - 129) = 0

Subtract the terms

More Steps

2 x^{2} + 43 - 86 x = 0

Rewrite in standard form

2 x^{2} - 86 x + 43 = 0

Substitute a= 2,b= - 86 and c= 43 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{86 \pm ( - 86 ) ^{2} - 4 \times 2 \times 43}{2 \times 2}

Simplify the expression

x = \frac{86 \pm ( - 86 ) ^{2} - 4 \times 2 \times 43}{4}

Simplify the expression

More Steps

x = \frac{86 \pm 7052}{4}

Simplify the radical expression

More Steps

x = \frac{86 \pm 2 1763}{4}

Separate the equation into 2 possible cases

x = \frac{86 + 2 1763}{4} x = \frac{86 - 2 1763}{4}

Simplify the expression

More Steps

x = \frac{43 + 1763}{2} x = \frac{86 - 2 1763}{4}

Simplify the expression

More Steps

x = \frac{43 + 1763}{2} x = \frac{43 - 1763}{2}

Solution

x_{1} = \frac{43 - 1763}{2}, x_{2} = \frac{43 + 1763}{2}

Alternative Form

x_{1} \approx 0.505953, x_{2} \approx 42.494047

Show Solution

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