Solve left(2x*3x-2000right)*left(30+100right)+2000*100=642000

$$\left( 2x \times 3x-2000 \right) \times \left( 30+100 \right) +2000 \cdot 100 = 642000$$

Solve for x

$$x=30$$

$$x=-30$$

Steps by Finding Square Root

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

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

Multiply 2 and 3 to get 6.

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

Add 30 and 100 to get 130.

$$\left(6x^{2}-2000\right)\times 130+2000\times 100=642000$$

Use the distributive property to multiply 6x^{2}-2000 by 130.

$$780x^{2}-260000+2000\times 100=642000$$

Multiply 2000 and 100 to get 200000.

$$780x^{2}-260000+200000=642000$$

Add -260000 and 200000 to get -60000.

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

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}.

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

Multiply 2 and 3 to get 6.

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

Add 30 and 100 to get 130.

$$\left(6x^{2}-2000\right)\times 130+2000\times 100=642000$$

Use the distributive property to multiply 6x^{2}-2000 by 130.

$$780x^{2}-260000+2000\times 100=642000$$

Multiply 2000 and 100 to get 200000.

$$780x^{2}-260000+200000=642000$$

Add -260000 and 200000 to get -60000.

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

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.

$$x=30 x=-30$$