Solve 49x^2-140+120=0

$$49 { x }^{ 2 } -140+120=0$$

Solve for x

$$x=\frac{2\sqrt{5}}{7}\approx 0.638876565$$

$$x=-\frac{2\sqrt{5}}{7}\approx -0.638876565$$

Steps by Finding Square Root

Add -140 and 120 to get -20.

$$49x^{2}-20=0$$

Add 20 to both sides. Anything plus zero gives itself.

$$49x^{2}=20$$

Divide both sides by 49.

$$x^{2}=\frac{20}{49}$$

Take the square root of both sides of the equation.

$$x=\frac{2\sqrt{5}}{7} x=-\frac{2\sqrt{5}}{7}$$

Steps Using the Quadratic Formula

Add -140 and 120 to get -20.

$$49x^{2}-20=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 49 for a, 0 for b, and -20 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 49\left(-20\right)}}{2\times 49}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 49\left(-20\right)}}{2\times 49}$$

Multiply -4 times 49.

$$x=\frac{0±\sqrt{-196\left(-20\right)}}{2\times 49}$$

Multiply -196 times -20.

$$x=\frac{0±\sqrt{3920}}{2\times 49}$$

Take the square root of 3920.

$$x=\frac{0±28\sqrt{5}}{2\times 49}$$

Multiply 2 times 49.

$$x=\frac{0±28\sqrt{5}}{98}$$

Now solve the equation x=\frac{0±28\sqrt{5}}{98} when ± is plus.

$$x=\frac{2\sqrt{5}}{7}$$

Now solve the equation x=\frac{0±28\sqrt{5}}{98} when ± is minus.

$$x=-\frac{2\sqrt{5}}{7}$$

The equation is now solved.

$$x=\frac{2\sqrt{5}}{7} x=-\frac{2\sqrt{5}}{7}$$