Solve x*1.5x=7560

$$x \times 1.5x=7560$$

Solve for x

$$x=12\sqrt{35}\approx 70.992957397$$

$$x=-12\sqrt{35}\approx -70.992957397$$

Steps by Finding Square Root

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

$$x^{2}\times 1.5=7560$$

Divide both sides by 1.5.

$$x^{2}=\frac{7560}{1.5}$$

Expand \frac{7560}{1.5} by multiplying both numerator and the denominator by 10.

$$x^{2}=\frac{75600}{15}$$

Divide 75600 by 15 to get 5040.

$$x^{2}=5040$$

Take the square root of both sides of the equation.

$$x=12\sqrt{35} x=-12\sqrt{35}$$

Steps Using the Quadratic Formula

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

$$x^{2}\times 1.5=7560$$

Subtract 7560 from both sides.

$$x^{2}\times 1.5-7560=0$$

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.

$$1.5x^{2}-7560=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1.5 for a, 0 for b, and -7560 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 1.5\left(-7560\right)}}{2\times 1.5}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 1.5\left(-7560\right)}}{2\times 1.5}$$

Multiply -4 times 1.5.

$$x=\frac{0±\sqrt{-6\left(-7560\right)}}{2\times 1.5}$$

Multiply -6 times -7560.

$$x=\frac{0±\sqrt{45360}}{2\times 1.5}$$

Take the square root of 45360.

$$x=\frac{0±36\sqrt{35}}{2\times 1.5}$$

Multiply 2 times 1.5.

$$x=\frac{0±36\sqrt{35}}{3}$$

Now solve the equation x=\frac{0±36\sqrt{35}}{3} when ± is plus.

$$x=12\sqrt{35}$$

Now solve the equation x=\frac{0±36\sqrt{35}}{3} when ± is minus.

$$x=-12\sqrt{35}$$

The equation is now solved.

$$x=12\sqrt{35} x=-12\sqrt{35}$$