Solve (65+78+96/54)x/60x=54

$$\frac { ( \frac { 65 + 78 + 96 } { 54 } ) x } { 60 } x = 54$$

Solve for x

$$x = \frac{108 \sqrt{3585}}{239} \approx 27.056426394$$

$$x = -\frac{108 \sqrt{3585}}{239} \approx -27.056426394$$

Steps by Finding Square Root

Multiply both sides of the equation by 60.

$$\frac{65+78+96}{54}xx=3240$$

Add 65 and 78 to get 143.

$$\frac{143+96}{54}xx=3240$$

Add 143 and 96 to get 239.

$$\frac{239}{54}xx=3240$$

Multiply x and x to get x^{2}.

$$\frac{239}{54}x^{2}=3240$$

Multiply both sides by \frac{54}{239}, the reciprocal of \frac{239}{54}.

$$x^{2}=3240\times \frac{54}{239}$$

Express 3240\times \frac{54}{239} as a single fraction.

$$x^{2}=\frac{3240\times 54}{239}$$

Multiply 3240 and 54 to get 174960.

$$x^{2}=\frac{174960}{239}$$

Take the square root of both sides of the equation.

$$x=\frac{108\sqrt{3585}}{239} x=-\frac{108\sqrt{3585}}{239}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 60.

$$\frac{65+78+96}{54}xx=3240$$

Add 65 and 78 to get 143.

$$\frac{143+96}{54}xx=3240$$

Add 143 and 96 to get 239.

$$\frac{239}{54}xx=3240$$

Multiply x and x to get x^{2}.

$$\frac{239}{54}x^{2}=3240$$

Subtract 3240 from both sides.

$$\frac{239}{54}x^{2}-3240=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{239}{54} for a, 0 for b, and -3240 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{239}{54}\left(-3240\right)}}{2\times \frac{239}{54}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{239}{54}\left(-3240\right)}}{2\times \frac{239}{54}}$$

Multiply -4 times \frac{239}{54}.

$$x=\frac{0±\sqrt{-\frac{478}{27}\left(-3240\right)}}{2\times \frac{239}{54}}$$

Multiply -\frac{478}{27} times -3240.

$$x=\frac{0±\sqrt{57360}}{2\times \frac{239}{54}}$$

Take the square root of 57360.

$$x=\frac{0±4\sqrt{3585}}{2\times \frac{239}{54}}$$

Multiply 2 times \frac{239}{54}.

$$x=\frac{0±4\sqrt{3585}}{\frac{239}{27}}$$

Now solve the equation x=\frac{0±4\sqrt{3585}}{\frac{239}{27}} when ± is plus.

$$x=\frac{108\sqrt{3585}}{239}$$

Now solve the equation x=\frac{0±4\sqrt{3585}}{\frac{239}{27}} when ± is minus.

$$x=-\frac{108\sqrt{3585}}{239}$$

The equation is now solved.

$$x=\frac{108\sqrt{3585}}{239} x=-\frac{108\sqrt{3585}}{239}$$