Solve 6x^2-2000=6420

$$6 { x }^{ 2 } -2000=6420$$

Solve for x

$$x = \frac{\sqrt{12630}}{3} \approx 37.461090926$$

$$x = -\frac{\sqrt{12630}}{3} \approx -37.461090926$$

Steps by Finding Square Root

Add 2000 to both sides.

$$6x^{2}=6420+2000$$

Add 6420 and 2000 to get 8420.

$$6x^{2}=8420$$

Divide both sides by 6.

$$x^{2}=\frac{8420}{6}$$

Reduce the fraction \frac{8420}{6} to lowest terms by extracting and canceling out 2.

$$x^{2}=\frac{4210}{3}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{12630}}{3} x=-\frac{\sqrt{12630}}{3}$$

Steps Using the Quadratic Formula

Subtract 6420 from both sides.

$$6x^{2}-2000-6420=0$$

Subtract 6420 from -2000 to get -8420.

$$6x^{2}-8420=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 6 for a, 0 for b, and -8420 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 6\left(-8420\right)}}{2\times 6}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 6\left(-8420\right)}}{2\times 6}$$

Multiply -4 times 6.

$$x=\frac{0±\sqrt{-24\left(-8420\right)}}{2\times 6}$$

Multiply -24 times -8420.

$$x=\frac{0±\sqrt{202080}}{2\times 6}$$

Take the square root of 202080.

$$x=\frac{0±4\sqrt{12630}}{2\times 6}$$

Multiply 2 times 6.

$$x=\frac{0±4\sqrt{12630}}{12}$$

Now solve the equation x=\frac{0±4\sqrt{12630}}{12} when ± is plus.

$$x=\frac{\sqrt{12630}}{3}$$

Now solve the equation x=\frac{0±4\sqrt{12630}}{12} when ± is minus.

$$x=-\frac{\sqrt{12630}}{3}$$

The equation is now solved.

$$x=\frac{\sqrt{12630}}{3} x=-\frac{\sqrt{12630}}{3}$$