Solve 96/10-6x^2/12=34/10

$$9 \frac { 6 } { 10 } - \frac { 6 x ^ { 2 } } { 12 } = 3 \frac { 4 } { 10 }$$

Solve for x

$$x = \frac{\sqrt{310}}{5} \approx 3.521363372$$

$$x = -\frac{\sqrt{310}}{5} \approx -3.521363372$$

Steps by Finding Square Root

Multiply both sides of the equation by 60, the least common multiple of 10,12.

$$6\left(9\times 10+6\right)-5\times 6x^{2}=6\left(3\times 10+4\right)$$

Multiply 9 and 10 to get 90.

$$6\left(90+6\right)-5\times 6x^{2}=6\left(3\times 10+4\right)$$

Add 90 and 6 to get 96.

$$6\times 96-5\times 6x^{2}=6\left(3\times 10+4\right)$$

Multiply 6 and 96 to get 576.

$$576-5\times 6x^{2}=6\left(3\times 10+4\right)$$

Multiply -5 and 6 to get -30.

$$576-30x^{2}=6\left(3\times 10+4\right)$$

Multiply 3 and 10 to get 30.

$$576-30x^{2}=6\left(30+4\right)$$

Add 30 and 4 to get 34.

$$576-30x^{2}=6\times 34$$

Multiply 6 and 34 to get 204.

$$576-30x^{2}=204$$

Subtract 576 from both sides.

$$-30x^{2}=204-576$$

Subtract 576 from 204 to get -372.

$$-30x^{2}=-372$$

Divide both sides by -30.

$$x^{2}=\frac{-372}{-30}$$

Reduce the fraction \frac{-372}{-30} to lowest terms by extracting and canceling out -6.

$$x^{2}=\frac{62}{5}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{310}}{5} x=-\frac{\sqrt{310}}{5}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 60, the least common multiple of 10,12.

$$6\left(9\times 10+6\right)-5\times 6x^{2}=6\left(3\times 10+4\right)$$

Multiply 9 and 10 to get 90.

$$6\left(90+6\right)-5\times 6x^{2}=6\left(3\times 10+4\right)$$

Add 90 and 6 to get 96.

$$6\times 96-5\times 6x^{2}=6\left(3\times 10+4\right)$$

Multiply 6 and 96 to get 576.

$$576-5\times 6x^{2}=6\left(3\times 10+4\right)$$

Multiply -5 and 6 to get -30.

$$576-30x^{2}=6\left(3\times 10+4\right)$$

Multiply 3 and 10 to get 30.

$$576-30x^{2}=6\left(30+4\right)$$

Add 30 and 4 to get 34.

$$576-30x^{2}=6\times 34$$

Multiply 6 and 34 to get 204.

$$576-30x^{2}=204$$

Subtract 204 from both sides.

$$576-30x^{2}-204=0$$

Subtract 204 from 576 to get 372.

$$372-30x^{2}=0$$

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.

$$-30x^{2}+372=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -30 for a, 0 for b, and 372 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-30\right)\times 372}}{2\left(-30\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-30\right)\times 372}}{2\left(-30\right)}$$

Multiply -4 times -30.

$$x=\frac{0±\sqrt{120\times 372}}{2\left(-30\right)}$$

Multiply 120 times 372.

$$x=\frac{0±\sqrt{44640}}{2\left(-30\right)}$$

Take the square root of 44640.

$$x=\frac{0±12\sqrt{310}}{2\left(-30\right)}$$

Multiply 2 times -30.

$$x=\frac{0±12\sqrt{310}}{-60}$$

Now solve the equation x=\frac{0±12\sqrt{310}}{-60} when ± is plus.

$$x=-\frac{\sqrt{310}}{5}$$

Now solve the equation x=\frac{0±12\sqrt{310}}{-60} when ± is minus.

$$x=\frac{\sqrt{310}}{5}$$

The equation is now solved.

$$x=-\frac{\sqrt{310}}{5} x=\frac{\sqrt{310}}{5}$$