Solve 19.2-40*0.24*0.8=2x^2

$$19.2 - 40 \times 0.24 \times 0.8 = 2 x ^ { 2 }$$

Solve for x

$$x=2.4$$

$$x=-2.4$$

Steps by Finding Square Root

Multiply 40 and 0.24 to get 9.6.

$$19.2-9.6\times 0.8=2x^{2}$$

Multiply 9.6 and 0.8 to get 7.68.

$$19.2-7.68=2x^{2}$$

Subtract 7.68 from 19.2 to get 11.52.

$$11.52=2x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$2x^{2}=11.52$$

Divide both sides by 2.

$$x^{2}=\frac{11.52}{2}$$

Expand \frac{11.52}{2} by multiplying both numerator and the denominator by 100.

$$x^{2}=\frac{1152}{200}$$

Reduce the fraction \frac{1152}{200} to lowest terms by extracting and canceling out 8.

$$x^{2}=\frac{144}{25}$$

Take the square root of both sides of the equation.

$$x=\frac{12}{5} x=-\frac{12}{5}$$

Steps Using the Quadratic Formula

Multiply 40 and 0.24 to get 9.6.

$$19.2-9.6\times 0.8=2x^{2}$$

Multiply 9.6 and 0.8 to get 7.68.

$$19.2-7.68=2x^{2}$$

Subtract 7.68 from 19.2 to get 11.52.

$$11.52=2x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$2x^{2}=11.52$$

Subtract 11.52 from both sides.

$$2x^{2}-11.52=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -11.52 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-11.52\right)}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-11.52\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-11.52\right)}}{2\times 2}$$

Multiply -8 times -11.52.

$$x=\frac{0±\sqrt{92.16}}{2\times 2}$$

Take the square root of 92.16.

$$x=\frac{0±\frac{48}{5}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±\frac{48}{5}}{4}$$

Now solve the equation x=\frac{0±\frac{48}{5}}{4} when ± is plus.

$$x=\frac{12}{5}$$

Now solve the equation x=\frac{0±\frac{48}{5}}{4} when ± is minus.

$$x=-\frac{12}{5}$$

The equation is now solved.

$$x=\frac{12}{5} x=-\frac{12}{5}$$