Solve 42x^2-2760-48000=0

$$42 x ^ { 2 } - 2760 - 48000 = 0$$

Solve for x

$$x = \frac{6 \sqrt{1645}}{7} \approx 34.764513927$$

$$x = -\frac{6 \sqrt{1645}}{7} \approx -34.764513927$$

Steps by Finding Square Root

Subtract 48000 from -2760 to get -50760.

$$42x^{2}-50760=0$$

Add 50760 to both sides. Anything plus zero gives itself.

$$42x^{2}=50760$$

Divide both sides by 42.

$$x^{2}=\frac{50760}{42}$$

Reduce the fraction \frac{50760}{42} to lowest terms by extracting and canceling out 6.

$$x^{2}=\frac{8460}{7}$$

Take the square root of both sides of the equation.

$$x=\frac{6\sqrt{1645}}{7} x=-\frac{6\sqrt{1645}}{7}$$

Steps Using the Quadratic Formula

Subtract 48000 from -2760 to get -50760.

$$42x^{2}-50760=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 42 for a, 0 for b, and -50760 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 42\left(-50760\right)}}{2\times 42}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 42\left(-50760\right)}}{2\times 42}$$

Multiply -4 times 42.

$$x=\frac{0±\sqrt{-168\left(-50760\right)}}{2\times 42}$$

Multiply -168 times -50760.

$$x=\frac{0±\sqrt{8527680}}{2\times 42}$$

Take the square root of 8527680.

$$x=\frac{0±72\sqrt{1645}}{2\times 42}$$

Multiply 2 times 42.

$$x=\frac{0±72\sqrt{1645}}{84}$$

Now solve the equation x=\frac{0±72\sqrt{1645}}{84} when ± is plus.

$$x=\frac{6\sqrt{1645}}{7}$$

Now solve the equation x=\frac{0±72\sqrt{1645}}{84} when ± is minus.

$$x=-\frac{6\sqrt{1645}}{7}$$

The equation is now solved.

$$x=\frac{6\sqrt{1645}}{7} x=-\frac{6\sqrt{1645}}{7}$$