Solve 4x/5+6/x+3x=0

$$\frac { 4 x } { 5 } + \frac { 6 } { x } + 3 x = 0$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{570}i}{19}\approx -0-1.256561725i$$

$$x=\frac{\sqrt{570}i}{19}\approx 1.256561725i$$

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 5x, the least common multiple of 5,x.

$$x\times 4x+5\times 6+3x\times 5x=0$$

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

$$x^{2}\times 4+5\times 6+3x\times 5x=0$$

Multiply 5 and 6 to get 30.

$$x^{2}\times 4+30+3x\times 5x=0$$

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

$$x^{2}\times 4+30+3x^{2}\times 5=0$$

Multiply 3 and 5 to get 15.

$$x^{2}\times 4+30+15x^{2}=0$$

Combine x^{2}\times 4 and 15x^{2} to get 19x^{2}.

$$19x^{2}+30=0$$

Subtract 30 from both sides. Anything subtracted from zero gives its negation.

$$19x^{2}=-30$$

Divide both sides by 19.

$$x^{2}=-\frac{30}{19}$$

The equation is now solved.

$$x=\frac{\sqrt{570}i}{19} x=-\frac{\sqrt{570}i}{19}$$

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 5x, the least common multiple of 5,x.

$$x\times 4x+5\times 6+3x\times 5x=0$$

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

$$x^{2}\times 4+5\times 6+3x\times 5x=0$$

Multiply 5 and 6 to get 30.

$$x^{2}\times 4+30+3x\times 5x=0$$

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

$$x^{2}\times 4+30+3x^{2}\times 5=0$$

Multiply 3 and 5 to get 15.

$$x^{2}\times 4+30+15x^{2}=0$$

Combine x^{2}\times 4 and 15x^{2} to get 19x^{2}.

$$19x^{2}+30=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 19 for a, 0 for b, and 30 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 19\times 30}}{2\times 19}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 19\times 30}}{2\times 19}$$

Multiply -4 times 19.

$$x=\frac{0±\sqrt{-76\times 30}}{2\times 19}$$

Multiply -76 times 30.

$$x=\frac{0±\sqrt{-2280}}{2\times 19}$$

Take the square root of -2280.

$$x=\frac{0±2\sqrt{570}i}{2\times 19}$$

Multiply 2 times 19.

$$x=\frac{0±2\sqrt{570}i}{38}$$

Now solve the equation x=\frac{0±2\sqrt{570}i}{38} when ± is plus.

$$x=\frac{\sqrt{570}i}{19}$$

Now solve the equation x=\frac{0±2\sqrt{570}i}{38} when ± is minus.

$$x=-\frac{\sqrt{570}i}{19}$$

The equation is now solved.

$$x=\frac{\sqrt{570}i}{19} x=-\frac{\sqrt{570}i}{19}$$