Solve 7x^2-3/4=141

$$\frac { 7 x ^ { 2 } - 3 } { 4 } = 141$$

Solve for x

$$x=9$$

$$x=-9$$

Steps Using Difference of Squares

Multiply both sides by 4.

$$7x^{2}-3=141\times 4$$

Multiply 141 and 4 to get 564.

$$7x^{2}-3=564$$

Subtract 564 from both sides.

$$7x^{2}-3-564=0$$

Subtract 564 from -3 to get -567.

$$7x^{2}-567=0$$

Divide both sides by 7.

$$x^{2}-81=0$$

Consider x^{2}-81. Rewrite x^{2}-81 as x^{2}-9^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-9\right)\left(x+9\right)=0$$

To find equation solutions, solve x-9=0 and x+9=0.

$$x=9 x=-9$$

Steps by Finding Square Root

Multiply both sides by 4.

$$7x^{2}-3=141\times 4$$

Multiply 141 and 4 to get 564.

$$7x^{2}-3=564$$

Add 3 to both sides.

$$7x^{2}=564+3$$

Add 564 and 3 to get 567.

$$7x^{2}=567$$

Divide both sides by 7.

$$x^{2}=\frac{567}{7}$$

Divide 567 by 7 to get 81.

$$x^{2}=81$$

Take the square root of both sides of the equation.

$$x=9 x=-9$$

Steps Using the Quadratic Formula

Multiply both sides by 4.

$$7x^{2}-3=141\times 4$$

Multiply 141 and 4 to get 564.

$$7x^{2}-3=564$$

Subtract 564 from both sides.

$$7x^{2}-3-564=0$$

Subtract 564 from -3 to get -567.

$$7x^{2}-567=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 7 for a, 0 for b, and -567 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 7\left(-567\right)}}{2\times 7}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 7\left(-567\right)}}{2\times 7}$$

Multiply -4 times 7.

$$x=\frac{0±\sqrt{-28\left(-567\right)}}{2\times 7}$$

Multiply -28 times -567.

$$x=\frac{0±\sqrt{15876}}{2\times 7}$$

Take the square root of 15876.

$$x=\frac{0±126}{2\times 7}$$

Multiply 2 times 7.

$$x=\frac{0±126}{14}$$

Now solve the equation x=\frac{0±126}{14} when ± is plus. Divide 126 by 14.

$$x=9$$

Now solve the equation x=\frac{0±126}{14} when ± is minus. Divide -126 by 14.

$$x=-9$$

The equation is now solved.

$$x=9 x=-9$$