Solve 556/126*x=6x

$$\frac{ 556 }{ 126 \times x } =6x$$

Solve for x

$$x=\frac{\sqrt{2919}}{63}\approx 0.857583661$$

$$x=-\frac{\sqrt{2919}}{63}\approx -0.857583661$$

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 126x.

$$556=6x\times 126x$$

Multiply x and x to get x^{2}.

$$556=6x^{2}\times 126$$

Multiply 6 and 126 to get 756.

$$556=756x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$756x^{2}=556$$

Divide both sides by 756.

$$x^{2}=\frac{556}{756}$$

Reduce the fraction \frac{556}{756} to lowest terms by extracting and canceling out 4.

$$x^{2}=\frac{139}{189}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{2919}}{63} x=-\frac{\sqrt{2919}}{63}$$

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 126x.

$$556=6x\times 126x$$

Multiply x and x to get x^{2}.

$$556=6x^{2}\times 126$$

Multiply 6 and 126 to get 756.

$$556=756x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$756x^{2}=556$$

Subtract 556 from both sides.

$$756x^{2}-556=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 756 for a, 0 for b, and -556 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 756\left(-556\right)}}{2\times 756}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 756\left(-556\right)}}{2\times 756}$$

Multiply -4 times 756.

$$x=\frac{0±\sqrt{-3024\left(-556\right)}}{2\times 756}$$

Multiply -3024 times -556.

$$x=\frac{0±\sqrt{1681344}}{2\times 756}$$

Take the square root of 1681344.

$$x=\frac{0±24\sqrt{2919}}{2\times 756}$$

Multiply 2 times 756.

$$x=\frac{0±24\sqrt{2919}}{1512}$$

Now solve the equation x=\frac{0±24\sqrt{2919}}{1512} when ± is plus.

$$x=\frac{\sqrt{2919}}{63}$$

Now solve the equation x=\frac{0±24\sqrt{2919}}{1512} when ± is minus.

$$x=-\frac{\sqrt{2919}}{63}$$

The equation is now solved.

$$x=\frac{\sqrt{2919}}{63} x=-\frac{\sqrt{2919}}{63}$$