Solve for x
x = \frac{200 \sqrt{3} + 100}{3} \approx 148.803387171
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Linear Equation
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\frac { 100 \sqrt { 3 } - x } { x - 100 } = \frac { 1 } { 2 }
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2\left(100\sqrt{3}-x\right)=x-100
Variable x cannot be equal to 100 since division by zero is not defined. Multiply both sides of the equation by 2\left(x-100\right), the least common multiple of x-100,2.
200\sqrt{3}-2x=x-100
Use the distributive property to multiply 2 by 100\sqrt{3}-x.
200\sqrt{3}-2x-x=-100
Subtract x from both sides.
200\sqrt{3}-3x=-100
Combine -2x and -x to get -3x.
-3x=-100-200\sqrt{3}
Subtract 200\sqrt{3} from both sides.
-3x=-200\sqrt{3}-100
The equation is in standard form.
\frac{-3x}{-3}=\frac{-200\sqrt{3}-100}{-3}
Divide both sides by -3.
x=\frac{-200\sqrt{3}-100}{-3}
Dividing by -3 undoes the multiplication by -3.
x=\frac{200\sqrt{3}+100}{3}
Divide -100-200\sqrt{3} by -3.
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