Solve 30(3x*2x-40*50)+100*3x*2x=642000

$$30(3x \times 2x-40 \times 50)+100 \times 3x \times 2x=642000$$

Solve for x

$$x=30$$

$$x=-30$$

Steps by Finding Square Root

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

$$30\left(3x^{2}\times 2-40\times 50\right)+100\times 3x\times 2x=642000$$

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

$$30\left(3x^{2}\times 2-40\times 50\right)+100\times 3x^{2}\times 2=642000$$

Multiply 3 and 2 to get 6.

$$30\left(6x^{2}-40\times 50\right)+100\times 3x^{2}\times 2=642000$$

Multiply 40 and 50 to get 2000.

$$30\left(6x^{2}-2000\right)+100\times 3x^{2}\times 2=642000$$

Use the distributive property to multiply 30 by 6x^{2}-2000.

$$180x^{2}-60000+100\times 3x^{2}\times 2=642000$$

Multiply 100 and 3 to get 300.

$$180x^{2}-60000+300x^{2}\times 2=642000$$

Multiply 300 and 2 to get 600.

$$180x^{2}-60000+600x^{2}=642000$$

Combine 180x^{2} and 600x^{2} to get 780x^{2}.

$$780x^{2}-60000=642000$$

Add 60000 to both sides.

$$780x^{2}=642000+60000$$

Add 642000 and 60000 to get 702000.

$$780x^{2}=702000$$

Divide both sides by 780.

$$x^{2}=\frac{702000}{780}$$

Divide 702000 by 780 to get 900.

$$x^{2}=900$$

Take the square root of both sides of the equation.

$$x=30 x=-30$$

Steps Using the Quadratic Formula

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

$$30\left(3x^{2}\times 2-40\times 50\right)+100\times 3x\times 2x=642000$$

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

$$30\left(3x^{2}\times 2-40\times 50\right)+100\times 3x^{2}\times 2=642000$$

Multiply 3 and 2 to get 6.

$$30\left(6x^{2}-40\times 50\right)+100\times 3x^{2}\times 2=642000$$

Multiply 40 and 50 to get 2000.

$$30\left(6x^{2}-2000\right)+100\times 3x^{2}\times 2=642000$$

Use the distributive property to multiply 30 by 6x^{2}-2000.

$$180x^{2}-60000+100\times 3x^{2}\times 2=642000$$

Multiply 100 and 3 to get 300.

$$180x^{2}-60000+300x^{2}\times 2=642000$$

Multiply 300 and 2 to get 600.

$$180x^{2}-60000+600x^{2}=642000$$

Combine 180x^{2} and 600x^{2} to get 780x^{2}.

$$780x^{2}-60000=642000$$

Subtract 642000 from both sides.

$$780x^{2}-60000-642000=0$$

Subtract 642000 from -60000 to get -702000.

$$780x^{2}-702000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 780 for a, 0 for b, and -702000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 780\left(-702000\right)}}{2\times 780}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 780\left(-702000\right)}}{2\times 780}$$

Multiply -4 times 780.

$$x=\frac{0±\sqrt{-3120\left(-702000\right)}}{2\times 780}$$

Multiply -3120 times -702000.

$$x=\frac{0±\sqrt{2190240000}}{2\times 780}$$

Take the square root of 2190240000.

$$x=\frac{0±46800}{2\times 780}$$

Multiply 2 times 780.

$$x=\frac{0±46800}{1560}$$

Now solve the equation x=\frac{0±46800}{1560} when ± is plus. Divide 46800 by 1560.

$$x=30$$

Now solve the equation x=\frac{0±46800}{1560} when ± is minus. Divide -46800 by 1560.

$$x=-30$$

The equation is now solved.

$$x=30 x=-30$$