Solve 45*x+12=8divx+12

$$45 \times x+12=8 \div x+12$$

Solve for x

$$x=\frac{2\sqrt{10}}{15}\approx 0.421637021$$

$$x=-\frac{2\sqrt{10}}{15}\approx -0.421637021$$

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 x.

$$45xx+x\times 12=8+x\times 12$$

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

$$45x^{2}+x\times 12=8+x\times 12$$

Subtract x\times 12 from both sides.

$$45x^{2}+x\times 12-x\times 12=8$$

Combine x\times 12 and -x\times 12 to get 0.

$$45x^{2}=8$$

Divide both sides by 45.

$$x^{2}=\frac{8}{45}$$

Take the square root of both sides of the equation.

$$x=\frac{2\sqrt{10}}{15} x=-\frac{2\sqrt{10}}{15}$$

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 x.

$$45xx+x\times 12=8+x\times 12$$

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

$$45x^{2}+x\times 12=8+x\times 12$$

Subtract 8 from both sides.

$$45x^{2}+x\times 12-8=x\times 12$$

Subtract x\times 12 from both sides.

$$45x^{2}+x\times 12-8-x\times 12=0$$

Combine x\times 12 and -x\times 12 to get 0.

$$45x^{2}-8=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 45 for a, 0 for b, and -8 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 45\left(-8\right)}}{2\times 45}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 45\left(-8\right)}}{2\times 45}$$

Multiply -4 times 45.

$$x=\frac{0±\sqrt{-180\left(-8\right)}}{2\times 45}$$

Multiply -180 times -8.

$$x=\frac{0±\sqrt{1440}}{2\times 45}$$

Take the square root of 1440.

$$x=\frac{0±12\sqrt{10}}{2\times 45}$$

Multiply 2 times 45.

$$x=\frac{0±12\sqrt{10}}{90}$$

Now solve the equation x=\frac{0±12\sqrt{10}}{90} when ± is plus.

$$x=\frac{2\sqrt{10}}{15}$$

Now solve the equation x=\frac{0±12\sqrt{10}}{90} when ± is minus.

$$x=-\frac{2\sqrt{10}}{15}$$

The equation is now solved.

$$x=\frac{2\sqrt{10}}{15} x=-\frac{2\sqrt{10}}{15}$$