Solve 260s^2-1705+240=0

$$260 s ^ { 2 } - 1705 + 240 = 0$$

Solve for s

$$s = \frac{\sqrt{3809}}{26} \approx 2.373734481$$

$$s = -\frac{\sqrt{3809}}{26} \approx -2.373734481$$

Steps by Finding Square Root

Add -1705 and 240 to get -1465.

$$260s^{2}-1465=0$$

Add 1465 to both sides. Anything plus zero gives itself.

$$260s^{2}=1465$$

Divide both sides by 260.

$$s^{2}=\frac{1465}{260}$$

Reduce the fraction \frac{1465}{260} to lowest terms by extracting and canceling out 5.

$$s^{2}=\frac{293}{52}$$

Take the square root of both sides of the equation.

$$s=\frac{\sqrt{3809}}{26} s=-\frac{\sqrt{3809}}{26}$$

Steps Using the Quadratic Formula

Add -1705 and 240 to get -1465.

$$260s^{2}-1465=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 260 for a, 0 for b, and -1465 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$s=\frac{0±\sqrt{0^{2}-4\times 260\left(-1465\right)}}{2\times 260}$$

Square 0.

$$s=\frac{0±\sqrt{-4\times 260\left(-1465\right)}}{2\times 260}$$

Multiply -4 times 260.

$$s=\frac{0±\sqrt{-1040\left(-1465\right)}}{2\times 260}$$

Multiply -1040 times -1465.

$$s=\frac{0±\sqrt{1523600}}{2\times 260}$$

Take the square root of 1523600.

$$s=\frac{0±20\sqrt{3809}}{2\times 260}$$

Multiply 2 times 260.

$$s=\frac{0±20\sqrt{3809}}{520}$$

Now solve the equation s=\frac{0±20\sqrt{3809}}{520} when ± is plus.

$$s=\frac{\sqrt{3809}}{26}$$

Now solve the equation s=\frac{0±20\sqrt{3809}}{520} when ± is minus.

$$s=-\frac{\sqrt{3809}}{26}$$

The equation is now solved.

$$s=\frac{\sqrt{3809}}{26} s=-\frac{\sqrt{3809}}{26}$$