Solve 52000a^2-12320=0

$$52000 a ^ { 2 } - 12320 = 0$$

Solve for a

$$a=\frac{\sqrt{1001}}{65}\approx 0.486747447$$

$$a=-\frac{\sqrt{1001}}{65}\approx -0.486747447$$

Steps by Finding Square Root

Add 12320 to both sides. Anything plus zero gives itself.

$$52000a^{2}=12320$$

Divide both sides by 52000.

$$a^{2}=\frac{12320}{52000}$$

Reduce the fraction \frac{12320}{52000} to lowest terms by extracting and canceling out 160.

$$a^{2}=\frac{77}{325}$$

Take the square root of both sides of the equation.

$$a=\frac{\sqrt{1001}}{65} a=-\frac{\sqrt{1001}}{65}$$

Steps Using the Quadratic Formula

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$52000a^{2}-12320=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 52000 for a, 0 for b, and -12320 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\times 52000\left(-12320\right)}}{2\times 52000}$$

Square 0.

$$a=\frac{0±\sqrt{-4\times 52000\left(-12320\right)}}{2\times 52000}$$

Multiply -4 times 52000.

$$a=\frac{0±\sqrt{-208000\left(-12320\right)}}{2\times 52000}$$

Multiply -208000 times -12320.

$$a=\frac{0±\sqrt{2562560000}}{2\times 52000}$$

Take the square root of 2562560000.

$$a=\frac{0±1600\sqrt{1001}}{2\times 52000}$$

Multiply 2 times 52000.

$$a=\frac{0±1600\sqrt{1001}}{104000}$$

Now solve the equation a=\frac{0±1600\sqrt{1001}}{104000} when ± is plus.

$$a=\frac{\sqrt{1001}}{65}$$

Now solve the equation a=\frac{0±1600\sqrt{1001}}{104000} when ± is minus.

$$a=-\frac{\sqrt{1001}}{65}$$

The equation is now solved.

$$a=\frac{\sqrt{1001}}{65} a=-\frac{\sqrt{1001}}{65}$$