Solve 2019x^2-72019=5*3

$$2019 x ^ { 2 } - 72019 = 5 \times 3$$

Solve for x

$$x = \frac{\sqrt{145436646}}{2019} \approx 5.973111287$$

$$x = -\frac{\sqrt{145436646}}{2019} \approx -5.973111287$$

Steps by Finding Square Root

Multiply 5 and 3 to get 15.

$$2019x^{2}-72019=15$$

Add 72019 to both sides.

$$2019x^{2}=15+72019$$

Add 15 and 72019 to get 72034.

$$2019x^{2}=72034$$

Divide both sides by 2019.

$$x^{2}=\frac{72034}{2019}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{145436646}}{2019} x=-\frac{\sqrt{145436646}}{2019}$$

Steps Using the Quadratic Formula

Multiply 5 and 3 to get 15.

$$2019x^{2}-72019=15$$

Subtract 15 from both sides.

$$2019x^{2}-72019-15=0$$

Subtract 15 from -72019 to get -72034.

$$2019x^{2}-72034=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2019 for a, 0 for b, and -72034 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2019\left(-72034\right)}}{2\times 2019}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2019\left(-72034\right)}}{2\times 2019}$$

Multiply -4 times 2019.

$$x=\frac{0±\sqrt{-8076\left(-72034\right)}}{2\times 2019}$$

Multiply -8076 times -72034.

$$x=\frac{0±\sqrt{581746584}}{2\times 2019}$$

Take the square root of 581746584.

$$x=\frac{0±2\sqrt{145436646}}{2\times 2019}$$

Multiply 2 times 2019.

$$x=\frac{0±2\sqrt{145436646}}{4038}$$

Now solve the equation x=\frac{0±2\sqrt{145436646}}{4038} when ± is plus.

$$x=\frac{\sqrt{145436646}}{2019}$$

Now solve the equation x=\frac{0±2\sqrt{145436646}}{4038} when ± is minus.

$$x=-\frac{\sqrt{145436646}}{2019}$$

The equation is now solved.

$$x=\frac{\sqrt{145436646}}{2019} x=-\frac{\sqrt{145436646}}{2019}$$