Solve 49+x^2-49/4/27x=49+4x^2-16/34x

$$\frac{ 49+ { x }^{ 2 } - \frac{ 49 }{ 4 } }{ 27x } = \frac{ 49+4 { x }^{ 2 } -16 }{ 34x }$$

Solve for x

$$x = \frac{\sqrt{26529}}{74} \approx 2.201043978$$

$$x = -\frac{\sqrt{26529}}{74} \approx -2.201043978$$

Steps by Finding Square Root

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 918x, the least common multiple of 27x,34x.

$$34\left(49+x^{2}-\frac{49}{4}\right)=27\left(49+4x^{2}-16\right)$$

Subtract \frac{49}{4} from 49 to get \frac{147}{4}.

$$34\left(\frac{147}{4}+x^{2}\right)=27\left(49+4x^{2}-16\right)$$

Use the distributive property to multiply 34 by \frac{147}{4}+x^{2}.

$$\frac{2499}{2}+34x^{2}=27\left(49+4x^{2}-16\right)$$

Subtract 16 from 49 to get 33.

$$\frac{2499}{2}+34x^{2}=27\left(33+4x^{2}\right)$$

Use the distributive property to multiply 27 by 33+4x^{2}.

$$\frac{2499}{2}+34x^{2}=891+108x^{2}$$

Subtract 108x^{2} from both sides.

$$\frac{2499}{2}+34x^{2}-108x^{2}=891$$

Combine 34x^{2} and -108x^{2} to get -74x^{2}.

$$\frac{2499}{2}-74x^{2}=891$$

Subtract \frac{2499}{2} from both sides.

$$-74x^{2}=891-\frac{2499}{2}$$

Subtract \frac{2499}{2} from 891 to get -\frac{717}{2}.

$$-74x^{2}=-\frac{717}{2}$$

Divide both sides by -74.

$$x^{2}=\frac{-\frac{717}{2}}{-74}$$

Express \frac{-\frac{717}{2}}{-74} as a single fraction.

$$x^{2}=\frac{-717}{2\left(-74\right)}$$

Multiply 2 and -74 to get -148.

$$x^{2}=\frac{-717}{-148}$$

Fraction \frac{-717}{-148} can be simplified to \frac{717}{148} by removing the negative sign from both the numerator and the denominator.

$$x^{2}=\frac{717}{148}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{26529}}{74} x=-\frac{\sqrt{26529}}{74}$$

Steps Using the Quadratic Formula

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 918x, the least common multiple of 27x,34x.

$$34\left(49+x^{2}-\frac{49}{4}\right)=27\left(49+4x^{2}-16\right)$$

Subtract \frac{49}{4} from 49 to get \frac{147}{4}.

$$34\left(\frac{147}{4}+x^{2}\right)=27\left(49+4x^{2}-16\right)$$

Use the distributive property to multiply 34 by \frac{147}{4}+x^{2}.

$$\frac{2499}{2}+34x^{2}=27\left(49+4x^{2}-16\right)$$

Subtract 16 from 49 to get 33.

$$\frac{2499}{2}+34x^{2}=27\left(33+4x^{2}\right)$$

Use the distributive property to multiply 27 by 33+4x^{2}.

$$\frac{2499}{2}+34x^{2}=891+108x^{2}$$

Subtract 891 from both sides.

$$\frac{2499}{2}+34x^{2}-891=108x^{2}$$

Subtract 891 from \frac{2499}{2} to get \frac{717}{2}.

$$\frac{717}{2}+34x^{2}=108x^{2}$$

Subtract 108x^{2} from both sides.

$$\frac{717}{2}+34x^{2}-108x^{2}=0$$

Combine 34x^{2} and -108x^{2} to get -74x^{2}.

$$\frac{717}{2}-74x^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$-74x^{2}+\frac{717}{2}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -74 for a, 0 for b, and \frac{717}{2} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-74\right)\times \frac{717}{2}}}{2\left(-74\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-74\right)\times \frac{717}{2}}}{2\left(-74\right)}$$

Multiply -4 times -74.

$$x=\frac{0±\sqrt{296\times \frac{717}{2}}}{2\left(-74\right)}$$

Multiply 296 times \frac{717}{2}.

$$x=\frac{0±\sqrt{106116}}{2\left(-74\right)}$$

Take the square root of 106116.

$$x=\frac{0±2\sqrt{26529}}{2\left(-74\right)}$$

Multiply 2 times -74.

$$x=\frac{0±2\sqrt{26529}}{-148}$$

Now solve the equation x=\frac{0±2\sqrt{26529}}{-148} when ± is plus.

$$x=-\frac{\sqrt{26529}}{74}$$

Now solve the equation x=\frac{0±2\sqrt{26529}}{-148} when ± is minus.

$$x=\frac{\sqrt{26529}}{74}$$

The equation is now solved.

$$x=-\frac{\sqrt{26529}}{74} x=\frac{\sqrt{26529}}{74}$$