Solve 30=x*145x

$$30=x \times 145x$$

Solve for x

$$x=\frac{\sqrt{174}}{29}\approx 0.454858826$$

$$x=-\frac{\sqrt{174}}{29}\approx -0.454858826$$

Steps by Finding Square Root

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

$$30=x^{2}\times 145$$

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

$$x^{2}\times 145=30$$

Divide both sides by 145.

$$x^{2}=\frac{30}{145}$$

Reduce the fraction \frac{30}{145} to lowest terms by extracting and canceling out 5.

$$x^{2}=\frac{6}{29}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{174}}{29} x=-\frac{\sqrt{174}}{29}$$

Steps Using the Quadratic Formula

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

$$30=x^{2}\times 145$$

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

$$x^{2}\times 145=30$$

Subtract 30 from both sides.

$$x^{2}\times 145-30=0$$

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.

$$145x^{2}-30=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 145 for a, 0 for b, and -30 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 145\left(-30\right)}}{2\times 145}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 145\left(-30\right)}}{2\times 145}$$

Multiply -4 times 145.

$$x=\frac{0±\sqrt{-580\left(-30\right)}}{2\times 145}$$

Multiply -580 times -30.

$$x=\frac{0±\sqrt{17400}}{2\times 145}$$

Take the square root of 17400.

$$x=\frac{0±10\sqrt{174}}{2\times 145}$$

Multiply 2 times 145.

$$x=\frac{0±10\sqrt{174}}{290}$$

Now solve the equation x=\frac{0±10\sqrt{174}}{290} when ± is plus.

$$x=\frac{\sqrt{174}}{29}$$

Now solve the equation x=\frac{0±10\sqrt{174}}{290} when ± is minus.

$$x=-\frac{\sqrt{174}}{29}$$

The equation is now solved.

$$x=\frac{\sqrt{174}}{29} x=-\frac{\sqrt{174}}{29}$$